Algebra 2 & Trigonometry Final Study Guide
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Algebra 2 & Trigonometry Final Study Guide Important Facts A function is a relation in which each element of the domain corresponds with exactly one element of the range. A function is one-to-one if each element of the range corresponds to exactly one x-value in the domain. The vertical line test states that if a vertical line passes through more than one point on a graph of a relation, then the relation is not a function. The horizontal line test states that if a horizontal line passes through more than one point on a graph of a function, then the function is not 1-1. Direct variation is a relationship that can be expressed as the function , where k is the constant of variation. Notice that solving for k results in the equation . The graph of a direct variation is a line that passes through the origin. A direct variation represents a constant rate of change (slope) with an initial value (y-intercept) of 0. Inverse variation is a relationship that can be expressed as the function , where k is the constant of variation. Notice that solving for k results in the equation where the product is constant. Where the constant is positive, a decrease in the value of one factor must accompany an increase in the value of the other factor. When two quantities vary inversely, as one quantity increases, the other decreases proportionally. The sum of the roots of a quadratic equation is . The product of the roots of a quadratic equation is . To complete the square add ( ) Number pairs of the form and are complex conjugates. On the graphs of and o || Amplitude o B is the frequency or the number of cycles from . o | | is the period of the function. , , , An arithmetic sequence follows a pattern of adding a fixed amount from one term to the next. A geometric sequence follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term. The binomial probability of x successes in n trials is n denotes the number of fixed trials x denotes the number of successes in the n trials p denotes the probability of success q denotes the probability of failure (1-p)
Transcript of Algebra 2 & Trigonometry Final Study Guide
Algebra 2 & Trigonometry Final Study Guide
Important Facts
A function is a relation in which each element of the domain corresponds with exactly one element of the range.
A function is one-to-one if each element of the range corresponds to exactly one x-value in the domain.
The vertical line test states that if a vertical line passes through more than one point on a graph of a relation, then the relation is not a function.
The horizontal line test states that if a horizontal line passes through more than one point on a graph of a function, then the function is not 1-1.
Direct variation is a relationship that can be expressed as the function , where k is the
constant of variation. Notice that solving for k results in the equation
. The graph of a
direct variation is a line that passes through the origin. A direct variation represents a constant rate of change (slope) with an initial value (y-intercept) of 0.
Inverse variation is a relationship that can be expressed as the function
, where k is the
constant of variation. Notice that solving for k results in the equation where the product is constant. Where the constant is positive, a decrease in the value of one factor must accompany an increase in the value of the other factor. When two quantities vary inversely, as one quantity increases, the other decreases proportionally.
The sum of the roots of a quadratic equation is
.
The product of the roots of a quadratic equation is
.
To complete the square add (
)
Number pairs of the form and are complex conjugates.
On the graphs of and o | | Amplitude o B is the frequency or the number of cycles from .
o |
| is the period of the function.
, , ,
An arithmetic sequence follows a pattern of adding a fixed amount from one term to the next.
A geometric sequence follows a pattern of multiplying a fixed amount (not zero) times each term to arrive at the following term.
The binomial probability of x successes in n trials is
n denotes the number of fixed trials
x denotes the number of successes in the n trials
p denotes the probability of success
q denotes the probability of failure (1-p)
Types of functions
When interest is compounded n times per year for t years at an interest rate of r, the principal, P, grows to the amount A given by the formula:
