Algebra 1 Common Core Student Edition, Grade 8-9

Grap h in g Rat ional

Fu n ct i o n s

Object ive To graph rational functions

@ Common Co r e St at e St and ar d s

F- I F. B. 4 For a function th a t models a relationship

between tw o quantities, interpret key features o f graphs

and ta b le s... and sketch graphs showing key fe a tu re s ..

Also A-CED.A.2

MP1, MP2, MP3, MP 4, MP 5

| Getting Ready! X C

What does

the graph tell

you about t h e

relationship

bet ween speed and

the time needed to

make t he t rip?

On any t r i p , t h e t im e you t r av el in a car

varies inversely with the car's average

sp eed. Th e f u n ct i o n t = ~ represents

the time it takes to travel 60 mi at

different rates. Will the graph ever

in t ersect t he horizontal axis? The

vertical axis? Explain your reasoning.

Si i SSSSS

Rate (miles per hour), r

mathematical Inverse variations are examples of rational functions. A rational function can

PRA CTICES be written in the form i , r f[x)rr \ polynomial , = polynomial, where the denominator cannot be 0.

Lesso n ^
Vocabulary
’• rational function
asymptote

Esse n t i a l U n d e r st a n d i n g To graph a rational function /(x), you need to

understand the graph's behavior near values of x where the function is undefined.

Any value of the variable that makes the denominator of a rational function equal to 0 is

an excluded value.

Thin k ,.,

Why are some values

of x excluded?

Division by 0 is

undefined. So any value

of x that makes the

denominator equal to 0

is excluded.

Id en t if yin g Ex clu d ed V alu es

What is the excluded value for each function?

5

0/0*0 =x - 2

x - 2 = 0

x = 2 *—

The excluded value is x = 2

Qy =

-3

Set the den o m in ato r.

equal to 0.

*— Solve for x. —>

x + 8

x + 8 = 0

x = -8

The excluded value is x = - 8.

Go t I t? 1. What is the excluded value for y =x + 7 •

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Po w er A l g eb r a.co m

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j Lesso n 11- 7 Graphing Rational Functions 705