Question

Graph each rational function using transformations.

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

Short answer

The graph for the given rational expression is

Step-by-step solution

Step 1. Given information

Given rational expression

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

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 $R\left(x\right)$does not exist.

Step 3. Graphing the given expression

$$\begin{gathered} Givenexpression \\ R\left(x\right)=1+\frac{2}{{(x-3)}^2} \\ thedomainofthefunctionincludesR-\left\{3\right\} \\ As.onx=3thevalueofR\left(x\right)doesnotexist. \end{gathered}$$

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

Now replace $xwithx-3$and multiply it with $2$.

Finally adding 1 to it we get,