Chapter 4: Q. 39 (page 225)

Graph each rational function using transformations.
$R (x) = 1 + \frac{2}{{(x - 3)}^{2}}$

Short Answer

Expert verified

The graph for the given rational expression is

Step by step solution

Step 1. Given information

Given rational expression

$R (x) = 1 + \frac{2}{{(x - 3)}^{2}}$

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.

Step 3. Graphing the given expression

$G i v e n e x p r e s s i o n R (x) = 1 + \frac{2}{{(x - 3)}^{2}} t h e d o m a i n o f t h e f u n c t i o n i n c l u d e s R - {3} A s . o n x = 3 t h e v a l u e o f R (x) d o e s n o t e x i s t .$

Therefore first we construct the graph of $R (x) = \frac{1}{x^{2}}$

Now replace $x w i t h x - 3$ and multiply it with $2$ .

Finally adding 1 to it we get,

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Graph each rational function using transformations.
$R (x) = 1 + \frac{2}{{(x - 3)}^{2}}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Graphing the given expression

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Graph each rational function using transformations.R(x)=1+2(x-3)2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Graphing the given expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Graph each rational function using transformations.
$R (x) = 1 + \frac{2}{{(x - 3)}^{2}}$