Chapter 9, Problem 18MCQ

To determine

To identify: the asymptote, domain, and range of the function

Answer to Problem 18MCQ

The Vertical asymptote: $x=6$ , Horizontal asymptote: $y=4$ , Domain: $\left\{x|x\ne -6\right\}$ and Range: $\left\{y|y\ne 4\right\}$

Explanation of Solution

Given information: The function is $f\left(x\right)=\frac{2}{x-6}+4$ and the graph shown below

  

Calculation:

The function $y=\frac{a}{x-h}$

The given function is equivalent to $f\left(x\right)=\frac{2}{x-6}+4$

So it has $a=2,h=-3\&k=4$

Thus, its graph has

Vertical asymptote: $x=6$

Horizontal asymptote: $y=4$

Domain: $\left\{x|x\ne -6\right\}$

Range: $\left\{y|y\ne 4\right\}$