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Chapter 4: Q. 39 (page 225)

Graph each rational function using transformations.

R(x)=1+2(x-3)2

Short Answer

Expert verified

The graph for the given rational expression is

Step by step solution

01

Step 1. Given information

Given rational expression

R(x)=1+2(x-3)2

02

Step 2. Write the concept

Graphing a rational expression using transformations involves checking for domains of the expression which allows us to know where the exact position of the graph lies.

Also, we need to check different points where the value of R(x)does not exist.

03

Step 3. Graphing the given expression

GivenexpressionR(x)=1+2(x-3)2thedomainofthefunctionincludesR-{3}As.onx=3thevalueofR(x)doesnotexist.

Therefore first we construct the graph of R(x)=1x2

Now replace xwithx-3and multiply it with 2.

Finally adding 1 to it we get,

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