Chapter 3.7, Problem 29E

To determine

To graph: the given equation using parent graph $f\left(x\right)$ , also describe the transformations and find the locations of new asymptotes.

Answer to Problem 29E

  

Location of new vertical asymptote is $x=-5$ .

Location of new horizontal asymptote is $y=-4$ .

Explanation of Solution

Given information:

  $\text{Parent function, }f\left(x\right)=\frac{1}{x}$

  $y=\frac{-4x+2}{x+5}$

Calculation:

Rewrite the function as shown below to recognize the changes easily.

  $y=22\left(\frac{1}{x+5}\right)-4$

The equation of transformation shows that $f\left(x\right)$ is moved 5 units left, stretched it by the factor of 22 and finally moved 4 units down. Thus, the graph of transformation and parent graph $f\left(x\right)$ is as follows:

  

The red color is of graph $f\left(x\right)$ and blue color is of graph after transformation of $f\left(x\right)$

The new vertical asymptote is at $x=-5$ and horizontal asymptote is $y=-4$ .