Algebra I

Ch. 1 NotesExpressions, Equations, and

Functions

Section 1-1: Variables and Expressions

Algebraic Expression-

Variable-

Term-

Exponent-

Base-

Section 1-1

Ex1) Write the verbal expression for each algebraic expressionsa) b)

Operation Verbal Phrases

Addition

Subtraction

Multiplication

Division

Section 1-1

Ex2) Write the algebraic expression for the verbal expression

a) A number t more than 6

b) 10 less than the product of 7 and f

c) Two thirds of v

Section 1-2: Order of Operations

Parenthesis and brackets

Exponents

Multiplication & Division

Addition &Subtraction

Section 1-2

Ex1) Evaluate the expression

Ex2) Evaluate each expressiona) b)

Section 1-2

c) d)

Ex3) Evaluate when x = 4, y = 5, z = 3a)

b)

Section 1-4: The Distributive Property

Distributive Property –

Ex1) Rewrite using the Distributive Propertya) 7(3w – 5) b)

Section 1-4: The Distributive Property

Distributive Property – For any numbers a, b, and c: a(b + c) = ab + acEx) 2(3 + 4) = (2 x 3) + (2 x 4)

Ex1) Rewrite using the Distributive Propertya) 7(3w – 5) b)

Section 1-4

Like Terms –

Simplest Form –

Ex2) Simplifya) 17u + 25u b)

c) d)

Section 1-4

Like Terms – terms that have the same variable part

Simplest Form – contains no parenthesis or like terms

Ex2) Simplifya) 17u + 25u b)

c) d)

Section 1-6: RelationsCoordinate Plane

Section 1-6: Plotting Points

Plot and label the following points on the graph, and identify the location of the point (I, II, III, IV, x-axis, y-axis, origin).A(3, 5)B(-2, 4)C(-1, -7)D(5, -8)E(3, 0)F(0, -6)

Section 1-6

Ordered Pair-

X-coordinate-

Y-coordinate

Relation

Domain-

Range-

Mapping

Section 1-6: Vocabulary

Ordered Pair- set of numbers of coordinates written in the form (x, y)

X-coordinate- the horizontal placement of the point

Y-coordinate- the vertical placement of the point

Relation- a set of ordered pairs

Domain- first number in the ordered pair (typically x), also called the input

Range- second number in the ordered pair (typically y), also called the output

Mapping- shows how each element of the domain is paired with an element in the range

Section 1-6: All the Same!

Ordered Pairs: (1, 2), (-2, 4), (0, 3)Table

Graph

MappingDomainRange

X Y

Section 1-6

Ex1) Express [(2,5), (-2,3), (5,-2), (-1,-2)] as a table, a graph, and mappingTABLE GRAPH

MAPPING

Determine the domain and range!

Section 1-6Independent Variable –

Dependent Variable –

Ex2) Identify the dependent and independent variablesa) The dance committee is selling tickets to the Fall Ball. The more

tickets they sell, the more money they can spend on decorations.

b) Generally, the average price of movie tickets had increased over time.

Section 1-6Independent Variable – the variable that determines the output

Dependent Variable – the variable whose value is dependent on the independent variable

Ex2) Identify the dependent and independent variablesa) The dance committee is selling tickets to the Fall Ball. The more tickets

they sell, the more money they can spend on decorations.

b) Generally, the average price of movie tickets had increased over time.

Section 1-7: Functions

Function – a relationship between input and output. For each input there is one outputEx1) Determine if the relationships are functionsa) Dom.Range b)-2 -30 63 9 c) {(2,1), (3,-2), (3,1), (2,-1)}4

Domain 1 3 5 1

Range 4 2 4 -4

Section 1-7Discrete Function –

Continuous Function –

Vertical Line Test -

Section 1-7

Ex2) Determine if whether -3x + y = 8 is a function

Function Notation -

Section 1-8: Interpreting Graphs of Functions

Intercepts –

Y – intercept –

X – intercept –

Line of Symmetry –

Section 1-8: Interpreting Graphs of Functions

Intercepts – the points on a graph that intersect with an axis

Y – intercept – the point where a graph crosses the y-axis

X – intercept – the point where a graph crosses the x-axis

Line of Symmetry – a vertical line the cuts a graph in half

Section 1-8

Ex1) For each graph:a) Identify as linear or nonlinearb) Estimate the interceptsc) Find symmetry (if possible)