Chapter 8.3, Problem 17MCQ

To determine

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

Answer to Problem 17MCQ

The Vertical asymptote: $x=-3$ , Horizontal asymptote: $y=0$ , Domain: $\left\{x|x\ne -3\right\}$ and Range: $\left\{y|y\ne 0\right\}$

Explanation of Solution

Given information: The function is $f\left(x\right)=\frac{5}{x+3}$ and the graph shown below

  

Calculation:

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

The given function is equivalent to

  $f\left(x\right)=\frac{5}{x-\left(-3\right)}$

So it has $a=5\&h=-3$

Thus, its graph has

Vertical asymptote: $x=-3$

Horizontal asymptote: $y=0$

Domain: $\left\{x|x\ne -3\right\}$

Range: $\left\{y|y\ne 0\right\}$