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assessment is Unit 2 test! Continue to study by reviewing the

vocabulary flash cards you’ve already made, doing the homework from the Wiki, and doing skill and word problems.

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TEST TOPICS Power functions Solve radical functions Polynomial functions

Division Zeros

Rational functions Domain, asymptotes, holes, intercepts

There will be one question from the last unit test.

RATIONAL FUNCTION A rational function is the quotient of two

polynomial functions and , where is nonzero.

The domain of a rational function is all real numbers excluding those values for which , or the zeroes of

RATIONAL FUNCTIONS

The reciprocal function, like many rational functions has parts that approach specific - and -values.

The lines representing those values are called asymptotes.

This is not piecewise.

GRAPH

What is the domain of this function? Is this continuous at ? What is the end behavior of ?

VERTICAL ASYMPTOTES

Vertical asymptotes can only exist where the domain of a function is discontinuous.

But just because a function is discontinuous at particular value of doesn’t mean it will form an asymptote, so check.

ASYMPTOTES

The line is a vertical asymptote of if approaches as approaches .

HORIZONTAL ASYMPTOTES Let be a rational function defined as:

and are polynomials with no common factors. Let have degree and have degree The graph may have 1 or 0 horizontal asymptotes

using these guidelines: If , the horizontal asymptote is . If , the horizontal asymptote is If there is no horizontal asymptote.

ASYMPTOTES

The line is a horizontal asymptote of if approaches as approaches .

FIND THE DOMAIN AND THE ASYMPTOTES

𝑓 (𝑥 )= 𝑥+4𝑥−3

CHECK WITH A GRAPH

FIND THE DOMAIN AND THE ASYMPTOTES

𝑔 (𝑥 )=8 𝑥2+5

4 𝑥2+1

CHECK WITH A GRAPH

FIND THE DOMAIN AND THE ASYMPTOTES

HOLES

Given the polynomial function:

What is the domain of this?

HOLES

YOU!

Find the Domain, Asymptotes, holes, and - and -intercepts

OBLIQUE/SLANT ASYMPTOTES

We call these oblique or slant asymptotes.

What does oblique mean? It means slanted. These occur when a graph approaches

a linear relationship at its ends.

OBLIQUE/SLANT ASYMPTOTES Let be a rational function defined as:

Where and and have no common factors other than . If , the graph has an oblique asymptote. It’s

determined by dividing the numerator and denominator:

The asymptote will run along the line .

SLANT ASYMPTOTE

We know this has a vertical asymptote at . Because , there are no horizontal

asymptotes. Because , there is a slant asymptote. Do the long division… Slant asymptote at .

CHECK THE GRAPH

DO MATH!

Determine any asymptotes, holes, intercepts, and the domain of the function

DO MATH!

Determine any asymptotes, holes, intercepts, and the domain of the function.

is a rational function with the form . Given the information that has zeros at , which of the following MUST be true?

I. has degree 3II. has asymptotes at III. has a domain

a) I onlyb) II onlyc) III onlyd) I and II onlye) I, II, and III

is a rational function with the form . Given the information that has zeros at , which of the following CAN be true?

I. has degree 3II. has asymptotes at III. has a domain

a) I onlyb) II onlyc) III onlyd) I and II onlye) I, II, and III

Given the rational equation , identify the equation of the horizontal asymptote:

a) There is no horizontal asymptote.

a) Given the rational equation , identify the equation of the horizontal asymptote:

b) There is no horizontal asymptote.

Given the rational equation , identify the equation of the horizontal asymptote:

a) 2

b) There is no horizontal asymptote.