Vocabulary Word Definition Example Section · Algebra Nation Glossary of Terms . Vocabulary Word...

Algebra Nation Glossary of Terms Vocabulary Word Definition Example Section

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"AND" inequality The compound inequality is true only if both statements are true −1 < 𝑥𝑥 < 2 2

"OR" inequality The compound inequality is true if at least one of the statements is true 𝑥𝑥 ≥ 9 or 𝑥𝑥 < 0 2

Absolute value Represents the distance of a number from zero on a number line |𝑥𝑥 + 1|, | − 5|, |2| 2

Absolute value function

A v-shaped graph that represents a function that contains an algebraic expression within absolute

value symbols 𝑓𝑓(𝑥𝑥) = |𝑥𝑥 + 1| 3

Addition Property of Equality

Property of equality that states that adding the same quantity to both sides of an equation

creates a different (but equivalent) equation

𝑥𝑥 − 3 = 10 𝑥𝑥 − 3 + 3 = 10 + 3 2

Addition Property of Inequality

Property of equality that states that adding the same amount to both sides of an inequality creates

a different, but equivalent, inequality

𝑥𝑥 − 3 < 10 𝑥𝑥 − 3 + 3 < 10 + 3 2

Algebraic equation

Can be a number sentence (when both expressions contain only numbers), but often

contains variables whose values have not been determined

2𝑥𝑥 + 7𝑦𝑦 = 13 2

Area model A visual model for multiplication; a rectangular

array used to find all the factor pairs of a number or an expression

𝑥𝑥 −2 2𝑥𝑥 2𝑥𝑥2 −4𝑥𝑥 5 5𝑥𝑥 −10

5

Arithmetic sequence

A sequence where each term is the sum of the previous term and a common difference, 𝑑𝑑

2, 5, 8, 11, … where the first term is 2 and the difference is 3 4

Associative Property of

Addition

Property that states that when adding numbers, changing the grouping of the numbers or terms

does not change the sum (𝑥𝑥 + 1) + 8 = 𝑥𝑥 + (8 + 1) 1


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Associative Property of

Multiplication

States that when multiplying numbers, changing the grouping of the numbers or terms does not

change the product. (3𝑥𝑥)𝑦𝑦 = 3(𝑥𝑥𝑦𝑦) 1

Axis of symmetry

A vertical line that goes through the vertex of a quadratic function and divides the parabola into two congruent halves, that are mirror images of

each other (in 𝑓𝑓(𝑥𝑥) = 𝑎𝑎𝑥𝑥2 + 𝑏𝑏𝑥𝑥 + 𝑐𝑐 the axis of symmetry is 𝑥𝑥 = − 𝑏𝑏

2𝑎𝑎)

The axis of symmetry is 𝑥𝑥 = 2.

5,6

Binomial An algebraic expression consisting of two terms 𝑥𝑥3 − 8 is a binomial, because it has two terms: 𝑥𝑥3 and 8. 1

Box plot

A box and whisker diagram that display the five-number summary for a data set (minimum, first

quartile, median, third quartile, and maximum values)

9


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Categorical data Data that are based on “qualities” such as color, taste, or texture, rather than measurements

Hair color data: {blonde, black, red, blonde, blonde, black, brown, red} 9,10

Causation When one event causes another to happen Hours of work and income: a change in hours worked causes a change in income 10

Center Value at the center or middle of a data set that can be the mean, median or mode

In data set {1, 2, 2, 2, 2, 3, 4, 5, 5, 9}, the center can be the mean (3.5), the median (2.5), or

the mode is (2). 9

Closed dot in a graph

The number represented by a closed dot is part of the solution set show a graph 2

Closure property

A set of numbers is said to be closed for a specific mathematical operation when the result obtained after performing the operation on two elements of the set always produces an element of the same

set

{natural numbers} if you add or multiply a natural number with another natural

number, you get a natural number (for example, 2 + 3 = 5 or 3 × 4 = 12), so it is

closed; but if you subtract or divide natural numbers you do not always get another

natural number (for example: 1 − 2 = −1; or 1 ÷ 2 = 0.5), which is not closed

3

Closure Property for Integers

Property that states that Integers are closed under addition, subtraction and multiplication, because the sum, difference or product of two integers is always an integer. They are NOT closed under

division because dividing two integers does not always result in an integer.

−2 + 6 = 4; 6 − 7 = −1; 3×5 = 15; 3 ÷ 5 =0.60 (and 0.60 is not an integer) 3

Coefficient A number used to multiply a variable 𝑥𝑥2 + 8𝑥𝑥 + 16, where 8 is the coefficient of 𝑥𝑥 in the term 8𝑥𝑥 1,4,10


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Combinations of Functions

The sum, difference, product, or quotient of functions

Let 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥 and 𝑔𝑔(𝑥𝑥) = 5. Sum: 𝑓𝑓(𝑥𝑥) + 𝑔𝑔(𝑥𝑥) = 2𝑥𝑥 + 5

Difference: 𝑓𝑓(𝑥𝑥) − 𝑔𝑔(𝑥𝑥) = 2𝑥𝑥 − 5 Product: Sum: 𝑓𝑓(𝑥𝑥) ∙ 𝑔𝑔(𝑥𝑥) = (2𝑥𝑥)(5)

Quotient: 𝑓𝑓(𝑥𝑥)𝑔𝑔(𝑥𝑥) = 2𝑥𝑥

5

3

Complete the square

A technique used to solve quadratic equations where a quadratic equation is written as the sum or

difference of a perfect square and a constant

𝑥𝑥2 + 6𝑥𝑥 + 16 = 0 𝑥𝑥2 + 6𝑥𝑥 = −16

𝑥𝑥2 + 6𝑥𝑥 + 9 = −16 + 9 (𝑥𝑥 + 3)2 = −7

(𝑥𝑥 + 3)2 + 7 = 0

5

Complex solutions

Non-real solutions; a parabola that does not intercept the x-axis is said to have complex

solutions

For 𝑥𝑥2 = −9, no real number can be squared to get −9 6

Compositions of functions

When a function becomes the input of another function, creating a new function

Let 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥 and 𝑔𝑔(𝑥𝑥) = 𝑥𝑥2 − 1. (𝑓𝑓 ∘ 𝑔𝑔)(𝑥𝑥) = 𝑓𝑓�𝑔𝑔(𝑥𝑥)� = 2(𝑥𝑥2 − 1) = 2𝑥𝑥2 − 2

This is read “𝑓𝑓 composed with 𝑔𝑔 of 𝑥𝑥. (𝑔𝑔 ∘ 𝑓𝑓)(𝑥𝑥) = 𝑔𝑔�𝑓𝑓(𝑥𝑥)� = (2𝑥𝑥)2 − 1 = 4𝑥𝑥2 − 1

This is read “𝑔𝑔 composed with 𝑓𝑓 of 𝑥𝑥.

3

Compound inequality

Contains at least two inequalities that are joined by either "and" or "or"

2 < 3 + 𝑥𝑥 < 10 −1 < 𝑥𝑥 < 7 2

Compressing a function

When a function is multiplied by a coefficient greater than zero but less than 1

𝑓𝑓(𝑥𝑥) = 𝑥𝑥2

𝑔𝑔(𝑥𝑥) =13𝑓𝑓(𝑥𝑥) =

13𝑥𝑥2

6, 7


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Conditional relative

frequency

A fraction that indicates how many members or items out of a group have a particular

characteristic

Music Preferences Rock R&B Total

Male 2

10= 0.2

810

= 0.8 1010

= 1.0

Female 6

10= 0.6

410

= 0.4 1010

= 1.0

Total 8

20= 0.4

1220

= 0.6 2020

= 1.0

10

Constant A fixed value within an equation or expression (a number or letter that stands for a fixed number) 𝑥𝑥2 + 8𝑥𝑥 + 16, where 16 is the constant 1, 4, 10

Constant of proportionality

A constant multiplier, 𝑘𝑘, used to define the proportional relationship between two variables

𝑥𝑥 2 4 6 𝑦𝑦 20 40 60

𝑘𝑘 =𝑦𝑦𝑥𝑥

=404

= 10 4

Continuous data Data that can take almost any numeric value over a continuous range

The data on the historical times for the 100-meter dash in the Olympics. 9


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Continuous function

A function that forms a line, allowing the x-values to be any point in the interval

2

Coordinate plane

A two-dimensional surface on which points, lines and curves can be plotted ; it has two scales,

called the x-axis (a horizontal number line) and y-axis (a vertical number line) and four quadrants

with positive and negative numbers in both axes.

6, 7

Correlation

A statistical relationship between two or more data

sets

The relationship between your final grade and the number of classes you missed 10


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Correlation coefficient

Often known as 𝑟𝑟; a measure of the strength and direction of the linear association between two

quantitative variables

The correlation between missed classes and final grade is 𝑟𝑟 = −0.639; which suggest

a moderate negative correlation, and as the number of classes missed increases, the

final grade decreases

10

Commutative Property of

Addition

Property that states that the order of the numbers or terms in a sum can be changed without

affecting the sum 𝑎𝑎 + 𝑏𝑏 + 2 = 𝑏𝑏 + 𝑎𝑎 + 2 1

Commutative Property of

Multiplication

Property that states that the order of the numbers or terms in a product can be changed without

affecting the product 2𝑥𝑥𝑦𝑦 = 2𝑦𝑦𝑥𝑥 1

Data Quantitative or categorical information collected for reference or analysis

Age of bus riders of Bus 4744 Bay Route : {14, 14, 15, 17, 13, 14, 13, 15, 16, 15, 12, 12, 14, 15} 9

Data set A collection of data

Age of bus riders of Bus 4744 Bay Route: {14, 14, 15, 17, 13, 14, 13, 15, 16, 15, 12, 12, 14, 15}

Age of bus drivers of Bus 4744 Bay Route :

{44, 33, 32, 45, 45}

9

Decay rate

The constant ratio for a quantity that decreases over time. In the function 𝑓𝑓(𝑥𝑥) = 𝑎𝑎(𝑏𝑏𝑥𝑥), the decay rate is 𝑏𝑏 if 𝑏𝑏 0 < 𝑏𝑏 < 1 and 𝑏𝑏 = 1 − 𝑟𝑟, where 𝑟𝑟 is the

rate

𝑓𝑓(𝑥𝑥) = 10 �12�2; 𝑏𝑏 = 0.5, which is 0 < 𝑏𝑏 < 1, so

the rate 𝑟𝑟 is 1 − 0.5 = 0.5 7


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Decreasing intervals

When reading a graph from left to right, as the 𝑥𝑥 values increase, the 𝑦𝑦 values decrease

The decreasing interval is (−∞, 0).

3, 6, 7

Degree of a monomial

The sum of the exponents of all the variables of a monomial

The degree of 3𝑥𝑥33𝑦𝑦2 is five, because the exponents of the monomial are 3 and 2,

and the sum of 3 and 2 is five. 1

Degree of a polynomial

The highest degree of any monomial or term in the polynomial

The degree of polynomial 𝑥𝑥2 + 8𝑥𝑥 + 16 is two, because 𝑥𝑥2 is the monomial with the

highest degree. 1, 8

Dependent variable

A variable whose variation depends on that of another (output, range)

ℎ(𝑡𝑡) = 450 − 2𝑡𝑡, where ℎ(𝑡𝑡) is height in feet, and it is the dependent variable (depends

on time 𝑡𝑡) 3, 6

Difference of two squares

A squared number or expression subtracted from another squared number or expression 𝑥𝑥2 − 4 = (𝑥𝑥 − 2)(𝑥𝑥 + 2) 5

Direct variation

A relationship between two variables (let's say 𝑥𝑥 and 𝑦𝑦) in which one is a constant multiple of the other, so as the 𝑥𝑥−value increases, the 𝑦𝑦−value

increases or decreases at the same rate, following the relationship 𝑦𝑦 = 𝑘𝑘𝑥𝑥

𝑦𝑦 = 4𝑥𝑥, as the 𝑥𝑥−value increases by one unit, the 𝑦𝑦−value increases by four units

𝑦𝑦 = −2𝑥𝑥, as the 𝑥𝑥−value increases by one unit, the 𝑦𝑦−value decreases by two units

4

Discrete data Data that contains a finite number of possible values

The number of cups damaged in a shipment of ten boxes to a restaurant. 9


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Discrete function This function does not form a line and allows the 𝑥𝑥-values to be only certain points in the interval

2

Discriminant The expression located under the radical in the

quadratic formula. The discriminant helps us determine the nature of the roots of the polynomial

In the quadratic formula 𝑥𝑥 = −𝑏𝑏±�𝑏𝑏2−4𝑎𝑎𝑐𝑐2𝑎𝑎 ;

(𝑏𝑏2 − 4𝑎𝑎𝑐𝑐) is the discriminant 6

Distribution A graph, list, or function showing all the possible

values (or intervals) of the data and how often they occur

In this example, the dot plot shows all test scores in Mr. Gray’s class and how often

they occur

9


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Distributive property

Property that states that multiplying a single term by two or more terms inside a set of parentheses yields

an equivalent expression

4(3𝑥𝑥 − 8) = 4(3𝑥𝑥) + 4(−8) = 12𝑥𝑥 − 32 1, 2, 5

Division Property of Equality

Property of equality that is used to divide the same quantity into both sides of an equation, creating a

different, but equivalent, equation

4𝑦𝑦 = 20; divide by 4 both sides 44𝑥𝑥 =

204

; so, 𝑥𝑥 = 5 2

Division Property of Inequality

Property of inequality that states that if the same amount is divided into both sides of an inequality, it

creates an equivalent inequality; but when we divide both sides of the inequality by a negative

number, the inequality sign changes

4𝑦𝑦 ≤ 20; divide by 4 both sides 44𝑥𝑥 ≤

204

So, 𝑥𝑥 ≤ 5

−4𝑦𝑦 ≤ 20; divide by −4 both sides

−4−4

𝑥𝑥 ≤20−4

So, flipping the sign 𝑥𝑥 ≥ −5

2

Domain The set of values of 𝑥𝑥 used for the input of the function

𝑥𝑥 2 4 6 𝑓𝑓(𝑥𝑥) 20 40 60

The domain of function 𝑓𝑓(𝑥𝑥) is {2, 4, 6}.

3, 6, 7, 8

Dot plot

A graphical representation where each data value is represented with a dot above a number line

9



Dotted line of an inequality

In a graph of an inequality with two variables that is either < or >, the dotted line shows that the points

on the line are NOT solutions to the systems

𝑦𝑦 > 𝑥𝑥 + 1

4

Elimination method

Add or subtract the equations in the system to get an equation in one variable (sometimes after

writing an equivalent system that will eliminate one of the variables when you add or subtract the

equations)

3𝑥𝑥 + 4𝑦𝑦 = 48.05 5𝑥𝑥 + 2𝑦𝑦 = 67.25

Multiply the second equation by −2 to eliminate 𝑦𝑦.

3𝑥𝑥 + 4𝑦𝑦 = 48.05 −10𝑥𝑥 − 4𝑦𝑦 = −134.50

−7𝑥𝑥 = −86.45 𝑥𝑥 = 12.35

Pick an equation from the original system above and substitute the 𝑥𝑥-value.

3𝑥𝑥 + 4𝑦𝑦 = 48.05 3(12.35) + 4𝑦𝑦 = 48.05

37.05 + 4𝑦𝑦 = 48.05 𝑦𝑦 = 2.75

4



Empirical rule

States that for a normal distribution, nearly all of the data will fall within three standard deviations of the

mean (68% within one standard deviation, 95% within two, and 99.7% within three)

𝜇𝜇 − 2𝜎𝜎 𝜇𝜇 − 𝜎𝜎 𝜇𝜇 𝜇𝜇 + 𝜎𝜎 𝜇𝜇 + 2𝜎𝜎

68%

95%

99.7%

9

End behavior The behavior of the graph of 𝑓𝑓(𝑥𝑥) as 𝑥𝑥 approaches positive infinity or negative infinity

as 𝑥𝑥 increases, 𝑦𝑦 increases

7, 8



Equation A statement that the values of two mathematical expressions are equal (indicated by the sign =)

3𝑥𝑥 + 2 = 𝑥𝑥 + 4 (the value of 3𝑥𝑥 + 2 equals the value of 𝑥𝑥 + 4)

1, 2, 3, 5

Equivalent expressions

Expressions that are the same, even though they may look a little different 3 + 4 = 6 + 1 (both are equal to 7) 1, 2

Equivalent system of equations

Two or more systems of equations that have the same solution

Original System Equivalent System

� 2𝑥𝑥 − 5𝑦𝑦 = 0−3𝑥𝑥 + 4𝑦𝑦 = −7 ⟹ �

𝑦𝑦 = 25 𝑥𝑥

𝑦𝑦 = 34𝑥𝑥 −

74

4

Evaluating a function

Replace (substitute) a number for the function's variable; finding the value of the expression for that

number 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 + 9; so 𝑓𝑓(4) = 4 + 9 = 13 3

Even function Has symmetry about the 𝑦𝑦-axis; if a function is even, then 𝑓𝑓(−𝑥𝑥) = 𝑓𝑓(𝑥𝑥).

3

Explicit formula A formula to solve for a term using the first term of the sequence and the fixed rule for the sequence

In arithmetic sequences: 𝑎𝑎𝑛𝑛 = 𝑎𝑎1 + (𝑛𝑛 − 1)𝑑𝑑 In geometric sequences: 𝑎𝑎𝑛𝑛 = 𝑎𝑎1𝑟𝑟𝑛𝑛−1

𝑛𝑛 = term number 𝑎𝑎𝑛𝑛 = nth term 𝑎𝑎1 = first term

𝑑𝑑 = common difference 𝑟𝑟 = common ratio

4, 7



Exponential decay

Occurs when the common ratio of the function is greater than zero and less than one, causing the output values to get smaller as the input values

increase

7

Exponential function

A function in which the independent variable appears as an exponent of a constant 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥 3, 7

Exponential growth

Occurs when the common ratio of the function is greater than on, causing the output values to get

larger as the input values increase

7



Exponential pattern

A pattern formed from plotted points that would form an exponential graph if they were connected

7

Exponential regression

An approach for modeling the exponential relationship between a scalar dependent variable,

𝑌𝑌, and one or more explanatory variables (or independent variables), 𝑋𝑋

The exponential regression equation fit to

this data is 𝑔𝑔(𝑥𝑥) = 23.30(1.62)𝑥𝑥.

10



Expression A mathematical phrase that can contain numbers, variables, and operators 2𝑥𝑥 + 7, 𝑥𝑥2 − 3𝑥𝑥 + 2, 7 + 2 1, 2, 5

Factor A number or quantity that when multiplied by another produces a given number or expression

4 × 2 = 8 (4 and 2 are factors, while 8 is the product) 5, 8

Factoring The process of finding the factors of an expression that can be multiplied together to get the original

expression

2𝑥𝑥2 − 13𝑥𝑥 + 15 (2𝑥𝑥 − 3) and (𝑥𝑥 − 5) are the factors 5, 8

First quartile A number representing the first 25% of the data {1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 8, 9}

The first quartile falls between 2 and 3 it is 2.5.

9

Frequency How often data value(s) occur or the “count” of the data values

8 students earned 85% on a quiz, so the frequency for 85% is 8. 9, 10

Function

A relationship between input and output, where each input has a single output

The miles are a function of the hours, so the function is 𝑓𝑓(𝑥𝑥) = 50𝑥𝑥, for every amount of

hours there is a single output of miles.

3, 8



Function model A function that fits a data set

The linear regression equation fit to this data is 𝑓𝑓(𝑥𝑥) = 176.32𝑥𝑥 − 380.47, and the

exponential regression equation fit to this data is 𝑔𝑔(𝑥𝑥) = 23.30(1.62)𝑥𝑥.

10

Function notation

Writing algebraic variables as functions of other variables, like f(x)=4x (which is read "the function of x equals 4x," so basically f takes x and multiplies it

by 4).

𝑓𝑓(𝑥𝑥) = 𝑥𝑥 − 2; 𝑔𝑔(𝑥𝑥) = 𝑥𝑥2; ℎ(𝑥𝑥) = 2𝑥𝑥 3, 4

Geometric sequence

A sequence of numbers in which each term is the product of the previous term and some real

number

Each term is twice the amount of the

previous term

7

Graph

A diagram showing the relation between variable quantities

3, 4, 7, 8



Graphing method in a

system of equation

Graphing both equations and find the point where they intercept (if any)

The solutions to this system are (−1, 0) and

(4,−5) based on the graph.

4

Greater Common Factor (GCF)

The greatest factor that divides two numbers

The factors that divide 24 and 36 are {1, 2, 3, 4, 6, 9, 12} and the GCF is 12. 5

Growth rate

The percentage change or change ratio of a specific variable within a specific time period, given a certain context. In the function 𝑓𝑓(𝑥𝑥) =𝑎𝑎(𝑏𝑏𝑥𝑥), the growth rate is 𝑏𝑏 if 𝑏𝑏 > 1 and 𝑏𝑏 = 1 + 𝑟𝑟,

where 𝑟𝑟 is the rate.

𝑓𝑓(𝑥𝑥) = 10(3)2; 𝑏𝑏 = 3, which is 𝑏𝑏 > 1, so the rate 𝑟𝑟 is 3 + 1 = 2 7



Histogram A bar-style data display showing the frequency of

data measured over intervals, rather than displaying each individual data value

9

Hypothesis A proposition, supposition or proposed explanation

made on the basis of reasoning with limited evidence

The sun is shining, so it must be warm.

If it’s raining, then the streets are wet. 7

Increasing intervals

When reading a graph from left to right, as the 𝑥𝑥 values increase, the 𝑦𝑦 values increase

The increasing interval is (0,∞)

3, 6, 7

Independent variable

A variable whose variation does not depend on that of another (input, domain)

ℎ(𝑡𝑡) = 450 − 2𝑡𝑡, where 𝑡𝑡 is time in seconds, and it is the independent variable 3, 6



Inequality

The relation between two expressions that are not equal, ” > “ means greater than, and “<” means

less than

𝑥𝑥 + 3 > 9 So, the sum of 𝑥𝑥 and three is greater than

nine 2

Input A value assigned to the known variable in a function 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 − 2, where 𝑥𝑥 is the input 3

Integers Any positive or negative number, including zero but with no fractional or decimal part {. . .−3,−2,−1, 0, 1, 2, 3, . . . } 1

Interquartile range

is the middle 50% of the data set; includes the data points that lie between the first quartile the third

one quartile; also known as IQR.

Consider the following data set: {5, 5, 6, 7, 8, 8, 8, 9, 10, 12, 12} IQR = 𝑄𝑄3 − 𝑄𝑄1 = 10 − 6 = 4

9

Interval A range of values or set of real numbers lying between two numbers

The interval [1, 5] or 1 − 5 includes all integers from 1 to 5 9

Inverse function

Reverses or undoes the action of another function

by interchanging the dependent and independent variables of the function for an appropriate set of

values of the dependent variable

The inverse of 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥 + 3 is 𝑓𝑓−1(𝑥𝑥) = 𝑥𝑥−32 .

So, 𝑓𝑓 = {(0, 3), (1, 5), (2, 7)} and 𝑓𝑓−1 = {(3, 0), (5, 1), (7, 2)}

3

Inverse variation A relationship between two variables so that as one

quantity increases, the other quantity decreases following the relationship 𝑦𝑦 = 𝑘𝑘 �1

𝑥𝑥� 𝑦𝑦 = 2

1𝑥𝑥

4

Irrational number

A real number that cannot be written as a simple

fraction (in the form a/b, where a and b are integers), and when written as a decimal, the

decimals do not terminate, nor do they repeat

√5, 𝜋𝜋 1



Joint frequency The counts in the body of a table


Male 10 8 18 Female 15 12 27

Total 25 20 45

So, there are ten males liking rock, eight males liking R&B, etc.

10

Leading coefficient of a

polynomial

The coefficient of the leading term in a polynomial equation

The leading coefficient of 𝑥𝑥2 + 8𝑥𝑥 + 16 is one. 1, 8

Leading term of a polynomial

The monomial or term with the highest degree in a

polynomial equation

The leading term of 𝑥𝑥2 + 8𝑥𝑥 + 16 is 𝑥𝑥2. 1

Linear function

When graphed, is a straight line that increases or decreases at a constant rate; the slope-intercept

form of a linear function is 𝑦𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏.

This is linear function 𝑓𝑓(𝑥𝑥) = 50𝑥𝑥, where 𝑥𝑥

are hours and 𝑓𝑓(𝑥𝑥) are miles.

3, 4, 7



Linear pattern A pattern formed by plotted points that would form a line if they were connected

7

Linear regression

An approach for modeling the linear relationship between a scalar dependent variable, 𝑌𝑌, and one

or more explanatory variables (or independent variables), 𝑋𝑋

The linear regression equation fit to this

data is 𝑓𝑓(𝑥𝑥) = 176.32𝑥𝑥 − 380.47.

10



Mapping diagram

Diagram that shows how the inputs of a function are related to its outputs

3

Marginal frequency The total frequency for any row or column


Male 10 8 18 Female 15 12 27

Total 25 20 45

There is a total of 25 people liking rock in the sample and 20 liking R&B; and there

are 18 males and 27 females in the sample.

10



Maximum of a graph

The highest point (vertex) on a graph when a parabola opens down; the point where the graph

changes from increasing to decreasing

The maximum is (6, 625).

6

Maximum value in a data set The largest data point in a set of data The maximum value of data set {4, 8, 7, 2} is

8. 9

Mean The average of the data values In data set {1, 2, 2, 5, 5, 9}, the mean is

1+2+2+5+5+96

=246

= 4 9

Median The number in the middle when the data in a set are ordered from least to greatest

In data set {1, 2, 2, 2, 2, 3, 4, 5, 5, 9}, the median is 2.5.

In data set {1, 2, 2, 2, 2, 3, 4, 5, 5}, the median is 2.

9



Minimum of a graph

The lowest point (vertex) on a graph when a parabola opens up; the point where the graph

changes from decreasing to increasing

The minimum is (1,−1).

6

Minimum value in data set The smallest data point The minimum value of data set {4, 8, 7, 2} is

2. 9

Mode The most frequently occurring value(s) in a data set In data set {1, 2, 2, 2, 2, 3, 4, 5, 5, 9}, the the mode is 2. 9

Monomial An algebraic expression consisting of one term 3𝑥𝑥33𝑦𝑦2 has one term and it is a monomial. 1

Multiplication Property of

Equality

Property of equality that is used to multiply both sides of an equation by the same quantity,

creating a different, but equivalent, equation

�12� 𝑥𝑥 = 10

2 ∙ �12� 𝑥𝑥 = 10 ∙ 2 𝑥𝑥 = 20

2

Multiplication Property of Inequality

Property of inequality that states that if the same amount is multiplied into both sides of an inequality,

it creates an equivalent inequality; but when we multiply both sides of the inequality by a negative

number, the inequality sign changes

�12� 𝑥𝑥 < 10 �− 1

2� 𝑥𝑥 < 10

2 ∙ �12� 𝑥𝑥 < 10 ∙ 2 −2 ∙ �− 1

2� 𝑥𝑥 < 10 ∙ −2 𝑥𝑥 < 20 𝑥𝑥 > −20

2



Multiplicity of roots

The number of times a given polynomial equation has a root at a given point

The function 𝑓𝑓(𝑥𝑥) = 𝑥𝑥(𝑥𝑥 − 2)2(𝑥𝑥 + 4) has three roots: −4, 0, 2. The roots 0 and −4 has multiplicity of one because each occurs

once, but the root 2 has multiplicity of two because the factor (𝑥𝑥 − 2) occurs twice

(the factor is raised to the second power)

8

Natural numbers

All positive integers greater than zero

{1, 2, 3, . . . . } 1

Neither even nor odd function

A function that does not have symmetry about the 𝑦𝑦-axis or the origin.

Negative Exponent Property

Property of equality that states that a number with a negative exponent should be moved to the other side of the fraction line and the exponent switched

to positive

3−2 =1

32=

19

1

4−3= 43 = 64

1



Negative slope The value of the slope in the function is negative; also, when a functions is decreasing.

𝑔𝑔(𝑥𝑥) = −2𝑥𝑥 + 3 has a negative slope in −2

4

No solution A function is said to have no solution when there is

no number that we could substitute for the variables that would make the equation true.

𝑥𝑥 + 2 = 𝑥𝑥 − 3 if you subtract 𝑥𝑥 both sides, 2 CAN'T BE equal to −3 2

Normal distribution

A way to describe a set of data in which most of the values are clustered in the middle and fewer

values are clustered in the tails

In normal distributions the mean, median, and mode of the data are equivalent

A graph of a normal distribution is often called a

bell curve

𝜇𝜇 − 2𝜎𝜎 𝜇𝜇 − 𝜎𝜎 𝜇𝜇 𝜇𝜇 + 𝜎𝜎 𝜇𝜇 + 2𝜎𝜎

9

Number sentence

A statement of equality between two numerical expressions

2 + 10 = 12 2 + 5 < 8 2

𝑔𝑔(𝑥𝑥)



Odd function A function that has symmetry about the origin; if a function is odd, then 𝑓𝑓(−𝑥𝑥) = −𝑓𝑓(𝑥𝑥)

3

One solution A parabola is said to have one solution when its vertex is on the 𝑥𝑥-axis

The parabola has one solution: (2, 0)

6

One-to-one function

A function where every output value corresponds to exactly one input value

Function 𝑓𝑓 = {(−1, 6), (0, 5), (3, 2), (7, 10)} is one-to-one, because every input value

corresponds to exactly one output value, and every output value corresponds to

exactly one input value.

3



Open dot in a graph

A number represented by an open dot is not part of the solution set

The open dot is on 2, which means 2 is not

part of the solution set {𝑥𝑥|𝑥𝑥 > 2}.

2

Operators Symbols that represent the act of adding, subtracting, multiplying, and/or dividing

𝑥𝑥 + 4 (operator is sum, to add) 3𝑥𝑥 (operator is multiplication, the product

of 3 and 𝑥𝑥) 1

Ordered pairs

A pair of numbers used to locate a point or a location on a coordinate plane; the first number

(usually x) tells how far to move horizontally and the second number (usually y) tells how far to move

vertically

The points (2, 1), (4, 2), (6, 3), (8, 4), and (10, 5) are ordered pairs.

2, 6

Outlier An extreme value in a data set that is very distant from the others

If you scored a 98 in a test where the rest of your classmates scored 76, 63, 58, 76, 65, 68, 63, 71, 76, 77, 77, 71, and 68, then your score

is an outlier.

9

(2, 1)

(4, 2)

(6, 3)

(8, 4)

(10, 5)



Output The value of a function given a certain value for the known variable

In 𝑓𝑓(𝑥𝑥) = 𝑥𝑥 − 2, 𝑓𝑓(𝑥𝑥) is the output. So, if 𝑥𝑥 =4, then the output of 𝑓𝑓(4) is 4 − 2 = 2. 3

Parabola A curved symmetrical U-shaped graph that is the graphic representation of a quadratic function; it

may open up or down

5, 6

Percentage An amount out of one hundred; to convert a

fraction into a percentage, convert to a decimal and multiply by one hundred

40% of 100 is 40; 36 = 50% 10

Perfect square trinomial

The resulting polynomial when a binomial is squared

(𝑎𝑎 + 𝑏𝑏)2 = 𝑎𝑎2 + 2𝑎𝑎𝑏𝑏 + 𝑏𝑏2 or (𝑥𝑥 + 2)2 = 𝑥𝑥2 + 4𝑥𝑥 + 4 5

Piecewise function

A function defined by multiple sub-functions at certain intervals of the domain

3



Polynomial An algebraic expression consisting of one term or

the sum of several terms that contain different powers of the same variable(s)

𝑥𝑥2 + 4𝑥𝑥 + 4 is a polynomial with three terms (also known as a trinomial) 1, 5, 8

Positive slope The value of the slope in a function is positive; when a function is increasing.

This is linear function 𝑓𝑓(𝑥𝑥) = 50𝑥𝑥, where 𝑥𝑥

are hours and 𝑓𝑓(𝑥𝑥) are miles, and the slope is positive, which is 50 miles per hour.

4

Power of a Power Property

States that to find a power of a power, multiply the exponents (𝑦𝑦2)4 = 𝑦𝑦8 1

Power of a Product Property

States that if there is more than one factor in parenthesis, with an exponent outside the

parenthesis, then the exponent is distributed to every term in the parenthesis

(𝑎𝑎𝑏𝑏)2 = 𝑎𝑎2𝑏𝑏2 1

Power of a Quotient Property

States that the power of a quotient is equal to the quotient obtained when the dividend and divisor

are each raised to the indicated power separately, before the division is performed

�𝑎𝑎𝑏𝑏�2

=𝑎𝑎2

𝑏𝑏2 1



Product of Powers Property

States that the product of two powers with the same base is the base raised to the sum of the

powers (exponents) 𝑥𝑥3 ∙ 𝑥𝑥2 = 𝑥𝑥5 1

Properties of equality

Properties that can be applied to equations to create equivalent equations

𝑥𝑥 + 4 = 8 − 𝑥𝑥 𝑥𝑥 + 4 − 2 = 8 − 𝑥𝑥 − 2 2

Properties of inequality

Properties and algebraic rules for manipulating inequalities without affecting what makes the

inequality true

𝑥𝑥 + 4 < 13 𝑥𝑥 + 4 − 2 < 13 − 2 2

Quadratic formula

The solution of the quadratic equation by using the numerical coefficients of the equation; so you can

solve 𝑎𝑎𝑥𝑥2 + 𝑏𝑏𝑥𝑥 + 𝑐𝑐 using:

𝑥𝑥 =−𝑏𝑏 ± �𝑏𝑏2 − 4𝑎𝑎𝑐𝑐

2𝑎𝑎

You can solve 2𝑥𝑥2 + 3𝑥𝑥 − 6 using:

𝑥𝑥 =−3 ± �32 − 4(2)(−6)

2(2)

5

Quadratic function

A non-linear function in which the independent variable is raised to the second power; when

graphed, forms a curved line called a parabola.

The function 𝑓𝑓(𝑥𝑥) = 𝑥𝑥2 is quadratic.

3, 5, 6, 7



Quantitative data

Data that can be measured and recorded numerically

Height in inches of the school girls’ varsity basketball team: 70.5, 65, 72, 67, 69.5, 71.5,

70.5, 64, 65, 68, 67, and 69.5. 9, 10

Quartile

Divides a sorted data set into four equal parts, so

that each part represents 14 . Of the data set; 25%

of the data within a data set.

9

Quotient of Powers Property

States that the quotient of two powers with the

same base is the base raised to the difference of the powers (exponents)

𝑎𝑎7

𝑎𝑎2= 𝑎𝑎5 1

Radical expressions

any expression containing a radical (√ ) symbol, which indicate the root of a number or expression

√2𝑥𝑥 − 3 indicates the square root of the expression 2𝑥𝑥 − 3

√𝑥𝑥 + 43 indicates the cubic root of the expression 𝑥𝑥 + 4

√𝑥𝑥34 indicates the fourth root of the expression 𝑥𝑥3

1

Range The set of values of 𝑦𝑦 calculated from the domain or the output of the function

𝑥𝑥 2 4 6

𝑓𝑓(𝑥𝑥) 20 40 60

The range of function 𝑓𝑓(𝑥𝑥) is {20, 40, 60}.

3, 6, 7, 8

Lower quartile

Upper quartile

Median



Rate of change A rate that describes how one quantity changes in relation to another quantity

In function 𝑔𝑔(𝑥𝑥) = −2𝑥𝑥 + 3 the rate of change is −2, which means that for every unit increase in the 𝑥𝑥, there is a two-unit

decrease in 𝑦𝑦.

4, 7

Rational exponents

When the power or the exponent raised on a number is in the form

𝑝𝑝𝑞𝑞

, where 𝑞𝑞 ≠ 0

In 412, the power or exponent on number 4 is

a rational number, 12.

In 𝑥𝑥23, the power or exponent on 𝑥𝑥 is a

rational number, 23.

1

Rational Exponent Property

Property that states that an expression raised to a rational number can be written as a rational

expression 𝑥𝑥𝑎𝑎𝑏𝑏 = √𝑥𝑥𝑎𝑎𝑏𝑏 = �√𝑥𝑥𝑏𝑏 �

𝑎𝑎

Rational number A real number including those with a fractional or

decimal part; it can be written in the form a/b, where a and b are integers

5, 3,−2,12

, 0.2 1

Real number A number that can be any of the following: natural

numbers, whole numbers, integers, rational numbers, irrational numbers

√3,−2,12

,𝜋𝜋, 5.1, 87 1

𝑔𝑔(𝑥𝑥)



Recursive formula A formula to solve for a term using the computation of all previous terms

In arithmetic sequences: 𝑎𝑎𝑛𝑛 = 𝑎𝑎1 + 𝑑𝑑 In geometric sequences: 𝑎𝑎𝑛𝑛 = 𝑎𝑎𝑛𝑛−1𝑟𝑟

𝑛𝑛 = term number 𝑎𝑎𝑛𝑛 = nth term 𝑎𝑎1 = first term

𝑑𝑑 = common difference 𝑟𝑟 = common ratio

4, 7

Reflecting a function

The process of multiplying a function by negative one

The function 𝑔𝑔(𝑥𝑥) = −𝑓𝑓(𝑥𝑥) is the result of

reflecting the function 𝑓𝑓(𝑥𝑥) = 𝑥𝑥2 − 11𝑥𝑥 + 30.

6, 7

𝑔𝑔(𝑥𝑥)

𝑓𝑓(𝑥𝑥)



Relative frequency

The result of dividing each count in the frequency table by the overall total

Birthdays of Students by Season

Birthday Season Frequency

Relative Frequency

Spring 8 8

40= 0.2

Summer 12 1240

= 0.3

Fall 13 1340

= 0.325

Winter 7 7

40= 0.175

The relative frequency of 0.2 is the ratio of students with a birthday in the Spring.

10

Relative maximum

The point on a graph where the interval changes from increasing to decreasing

3



Relative minimum The point on a graph where the interval changes from decreasing to increasing

3

Residual The vertical distance between an actual data

point and the predicted value of the function fitted to the data

10

Residual plot A graph of the residuals (𝑦𝑦-axis) versus 𝑥𝑥-values (𝑥𝑥-axis)

This is the residual plot for the linear function 𝑓𝑓(𝑥𝑥) = 176.32𝑥𝑥 − 380.47.

10



Root of a polynomial

The solution(s) of the polynomial when the polynomial expression is equal to zero

The roots of polynomial 𝑥𝑥2 − 7𝑥𝑥 + 12 are 3 and 4, because when 𝑥𝑥2 − 7𝑥𝑥 + 12 = 0, this is equivalent to (𝑥𝑥 − 4)(𝑥𝑥 − 3) = 0, so 𝑥𝑥 = 3

and 𝑥𝑥 = 4.

8

Scatterplot A graphical representation of the relationship between two quantitative variables

10

Sequence

An set of numbers arranged in such a way that each successive number in the sequence is

defined by a fixed rule related to the position in the sequence or the previous number, or numbers, in

the sequence

The set {2, 4, 6, 8, 10, … } is a sequence where two units are added to each term to get

the next one; whereas the set {2, 4, 8, 16, 32, … } is a sequence where two

units are multiplied to each term to get the next one.

4



Shaded area of an inequality

The solution set in a graph of an inequality that has two variables

The shaded area represents all of the

possible combinations of soccer balls and basketballs that Coach De Leon could buy

with his budget.

4

Shape Describes the type or appearance of a graph:

symmetrical, with multiple peaks, skewed to the left or right, uniform, etc.

The following distributions have different means and standard deviations so their

shapes look different.

9



Shifting a function

Adding or subtracting a constant to the independent variable of a function will shift the

function left or right; adding or subtracting a constant to/from the dependent variable will shift

the function up or down.

The function 𝑔𝑔(𝑥𝑥) is the result of shifting the function 𝑓𝑓(𝑥𝑥) eight units to the left, so that

𝑔𝑔(𝑥𝑥) = 𝑓𝑓(𝑥𝑥 + 8).

6, 7

𝑔𝑔(𝑥𝑥) 𝑓𝑓(𝑥𝑥)



Simple linear regression

An approach for modeling the linear relationship between a scalar dependent variable, Y, and one explanatory variables (or independent variables), X

The linear regression equation for this data

is 𝑦𝑦 = 176.32𝑥𝑥 − 380.47, where 𝑦𝑦 is the number of Instagram posts and 𝑥𝑥

represents the months.

10

Skewed data

Data that have a long tail on one side or the other; a data set in which mean is greater or less than

median

If we have this data set about income per hour {$9.50, $10.25, $8.90, $10.25, $10.00, $9.00,

$17.00, $19.25, $18.50, $19.00, $10.50, $9.75}, the data is skewed towards the lower

salaries in the $9 − $10 range.

9



Slope

A measure of the steepness of a line or a section of a line calculated by connecting two points and dividing the change in the dependent values by

the change in the independent values

The slope of this line is 50.

4

Slope-intercept form

Takes the form of 𝑦𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏 and represents the equation of a line with a slope of 𝑚𝑚 and and a 𝑦𝑦-

intercept of 𝑏𝑏

The equation 𝑦𝑦 = −3𝑥𝑥 + 5 is in slope-intercept form, where the slope is −3 and

the 𝑦𝑦-intercept is 5. 4

Solid line of an inequality

In a graph of an inequality with two variables that are either ≤ or ≥, the solid line shows that the points

on the line are solutions to the inequality

18𝑠𝑠 + 20𝑏𝑏 ≤ 150

4



Solution of a system

Any ordered pair that makes all equations in the system true

� 2𝑥𝑥 − 5𝑦𝑦 = 0−3𝑥𝑥 + 4𝑦𝑦 = −7

The solution to the system shown above is (5, 2).

� 2(5) − 5(2) = 10 − 10 = 0−3(5) + 4(2) = −15 + 8 = −7

4, 6

Solution of an inequality

All the values of the variable that make an inequality a true statement

𝑥𝑥 + 3 > 9 𝑥𝑥 > 6

so the solution is {𝑥𝑥|𝑥𝑥 > 6} or (6,∞) 2, 4

Solution set The set of all the solutions of an equation or an inequality {−3, 8} or {(0,1), (1,2), (2,3), (3,4)} or {𝑥𝑥|𝑥𝑥 < 1} 2, 5

Solution to a system of

inequalities

Ordered pair(s) that is(are) a solution to all inequalities in the system; the area where the

shaded areas of the inequalities overlap

� 2𝑥𝑥 − 5𝑦𝑦 ≥ 0−3𝑥𝑥 + 4𝑦𝑦 < −6

A solution to the system shown above is (5, 2).

� 2(5) − 5(2) ≥ 0−3(5) + 4(2) < −6

(5, 2) is true for both inequalities.

4

Spread Describes variance in the data

The variance in this plot looks symmetrical and all data points are distributed around

the center.

9

Square roots The inverse operation of squaring a number, term, or polynomial

√9 = 3 The square root of nine is three (and three

squared is nine). 5



Standard deviation

The typical distance of the data values from the mean

The standard deviation for this data set:

is larger (more spread out) than for this

data set:

9

Standard form of a polynomial

When the monomial terms of a polynomial expression are organized in descending degree

order from left to right

The standard form of 𝑥𝑥2 − 11 + 3𝑥𝑥 + 3𝑥𝑥3 is 3𝑥𝑥3 + 𝑥𝑥2 + 3𝑥𝑥 − 11. 1

Standard form of a quadratic

equation

The sum of a quadratic term, a linear term, and a constant in the form of 𝑦𝑦 = 𝑎𝑎𝑥𝑥2 + 𝑏𝑏𝑥𝑥 + 𝑐𝑐

The quadratic equation 𝑦𝑦 = 𝑥𝑥2 + 2𝑥𝑥 + 1 is in standard form, where 𝑎𝑎 = 1, 𝑏𝑏 = 2, and 𝑐𝑐 = 1, whereas the quadratic equation 𝑦𝑦 = 2(𝑥𝑥 − 3)2 + 5 is not in standard form.

5

Statistics The science of collecting, organizing, and analyzing data

Data collected on number of books read: 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7

9



Stretching a function

Multiplying a function by a coefficient greater than 1

The function displayed with a solid line was stretched and displayed as the function

with the dashed line. Just like as 𝑔𝑔(𝑥𝑥) = 3𝑓𝑓(𝑥𝑥)

6, 7

Substitution method

Solving one of the equations for one of the variables, and then substituting the result into the other equation to have only one variable to solve

for

� 𝑦𝑦 = 2𝑥𝑥 − 1𝑦𝑦 = −3𝑥𝑥 + 9

Solve for 𝑥𝑥 first:

2𝑥𝑥 − 1 = −3𝑥𝑥 + 9 𝑥𝑥 = 2

So, � 𝑦𝑦 = 2(2) − 1𝑦𝑦 = −3(2) + 9

�𝑦𝑦 = 3𝑦𝑦 = 3

4



Subtraction Property of

Equality

Property of equality that is used to subtract the same quantity from both sides of an equation, creating a different, but equivalent, equation

𝑥𝑥 + 4 = 12 𝑥𝑥 + 4 − 4 = 12 − 4 2

Subtraction Property of Inequality

Property of equality that is used to subtract the same quantity from both sides of an inequality, creating a different, but equivalent, inequality

𝑥𝑥 + 4 ≥ 12 𝑥𝑥 + 4 − 4 ≥ 12 − 4 2

Successive approximations

A problem-solving method used to find/approximate a solution of a system of

equations, where the output values are examined to find the smallest absolute difference measured

to the given unit

We can approximate for what value of 𝑥𝑥

the functions are equal, by looking for the 𝑥𝑥-coordinates that have the

smallest absolute differences (to the nearest tenth) in 𝑓𝑓(𝑥𝑥)

and 𝑔𝑔(𝑥𝑥). So, for 𝑥𝑥 = 1.5 we can see a difference of 0.25 between 𝑓𝑓(𝑥𝑥) and 𝑔𝑔(𝑥𝑥), which means that the solution is closed to

𝑥𝑥 = 1.5.

6



Symmetrical (in statistics)

Having sides or halves that are the same and reflect one another; in a symmetrical distribution, its

mean is equal to its median

𝜇𝜇 Median

9

System of equations

A collection of two or more equations that are related and have the same set of variables or

unknowns � 𝑦𝑦 = 2𝑥𝑥 − 1𝑦𝑦 = −3𝑥𝑥 + 9 4, 6

System of inequalities

A collection of two or more inequalities that are related and have the same set of variables or

unknowns

𝑦𝑦 ≥ 𝑥𝑥 + 9 𝑦𝑦 > −4𝑥𝑥 − 10

4



System with infinitely many

solutions

A system with equations that have the same slope and same y-intercept

� 𝑦𝑦 = 2𝑥𝑥 − 1−4𝑥𝑥 + 2𝑦𝑦 = −2

Both equations have the same slope of 2 and the same 𝑦𝑦-intercept of − 1.

4

System with no solution system

A system with equations that have the same slope but different y-intercepts

� 𝑦𝑦 = 2𝑥𝑥 − 1−4𝑥𝑥 + 2𝑦𝑦 = −6

Both equations have the same slope of 2 , but different 𝑦𝑦-intercepts of −1 and −3.

4

Table of values Input and output values that are true for a given function and organized in a table

6

Term A constant, variable, or multiplicative combination of the two 4𝑥𝑥 − 5𝑦𝑦 + 9 has three terms (4𝑥𝑥, −5𝑦𝑦, and 9) 1, 4, 5

Third quartile A number representing the first 75% of the data In the set {1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 8, 9}, the third quartile falls between 6 and 7, so it is 6.5. 9

Transformation It occurs when an operation is performed on the dependent or the independent variable

The functions 𝑔𝑔(𝑥𝑥) = 𝑓𝑓(𝑥𝑥 − 1) and ℎ(𝑥𝑥) = 𝑓𝑓(𝑥𝑥) + 7 are transformations of a function 𝑓𝑓(𝑥𝑥). For example, if 𝑓𝑓(𝑥𝑥) = 2𝑥𝑥,

then ℎ(𝑥𝑥) = 2𝑥𝑥 + 7.

3, 7

Trinomial An algebraic expression consisting of three terms 𝑥𝑥2 + 8𝑥𝑥 + 16 has three terms (𝑥𝑥2, 8𝑥𝑥, 𝑎𝑎𝑛𝑛𝑑𝑑 16) and it is a trinomial. 1, 5

Truth values True and false number sentences or statements 4 + 13 = 17 is a true number sentence, whereas 3 + 13 = 14 is a false number

sentence. 2



Two solutions A parabola that intercepts the 𝑥𝑥-axis twice is said to have two solutions

This function has two solutions: 𝑥𝑥 = 1 and

𝑥𝑥 = 3, or (1, 0) and (3, 0).

6

Two-way frequency table

A visual representation of the frequency counts for two categorical variables; a contingency table

10

Unit of Measurement

A standard of measurement and exchange used to express a quantity

3 in (inches is the unit of measurement) 4.5 ft (feet in the unit of measurement) 1

Variable A letter that represents a quantity that may change within the context of a problem

In the equation, 3𝑥𝑥 + 2 = 𝑥𝑥 + 4, the variable is 𝑥𝑥.

1, 2, 3, 9



Vertex The maximum or minimum point of a parabola

The vertex of this function is (2,−1).

5, 6, 7

Vertex form Given 𝑎𝑎(𝑥𝑥 − ℎ)² + 𝑘𝑘, (ℎ,𝑘𝑘) is the vertex of a parabola

Given 2(𝑥𝑥 − 1)² + 9, (1, 9) is the vertex of the parabola. 6

Vertical line test

A way to test if a graph represents a function: if a vertical line drawn anywhere on a graph hits the graph in more than one place, then the graph is not a function since this shows an input value, 𝑥𝑥,

has more than one output value, 𝑦𝑦

For this function, if a vertical line is drawn anywhere, it will hit the graph only once!

3



Whole numbers Positive integers greater than or equal to zero; whole numbers cannot be negative or fractions {0,1,2,3. . . } 1

𝑥𝑥-intercept On a graph, the value of 𝑥𝑥 at the point where the

line crosses the 𝑥𝑥-axis; this happens when the value of 𝑦𝑦 is zero

In this graph the 𝑥𝑥-intercept is 1.5.

5, 6, 7

𝑦𝑦-intercept On a graph, the value of 𝑦𝑦 at the point where the

line crosses the 𝑦𝑦-axis; this happens when the value of 𝑥𝑥 is zero

In this graph the 𝑦𝑦-intercept is 3.

4, 5, 6, 7, 10

Zero Product Property

Property that states that when the product of two or more factors equals zero, one or more of the

factors must also equal zero

If 𝑥𝑥𝑦𝑦 = 0, then either 𝑥𝑥 = 0, 𝑦𝑦 = 0, or both If (𝑥𝑥 + 2)(𝑥𝑥 − 3) = 0; then either 𝑥𝑥 + 2 = 0 or

𝑥𝑥 − 3 = 0, or both 1, 2, 5



Zero(s) of a function

Equivalent to the 𝑥𝑥-intercept, the value(s) of 𝑥𝑥 that make(s) the value of function equal to zero; the solutions to a function when the function is set to

zero.

The zeros of this function are 1 and 3.

5, 6, 8

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