Question

Use the rules of transformations to compare the graphs of the functions, f(x) = 1/x and g(x) = 5/x-1. Which of the following options represents the asymptotes of the functions, f(x) and g(x)?
Select all that apply.
x = 2
x = -1
y = 0
y = 1
y = -1

Answer 1

Answer: The Horizontal asymptote of f(x) and g(x) is y=0. The third option is correct.

Explanation:

it is given that the using the rules of transformations to compare the graphs of the functions,

$f(x)=\frac{1}{x}$

$g(x)=\frac{5}{x-1}$

The graph of f(x) vertically stretch by factor 5 and shifts 1 unit right to transform g(x).

To find vertical asymptotes equate denominator equal to 0.

$x=0$

$x=1$

Therefore the function f(x) has vertical asymptote x=0, and g(x) has vertical asymptote x=1. So their is not common vertical asymptote.

To find horizontal asymptotes put $x=\infty$.

$f(x)\rightarrow 0\text{ as }x\rightarrow \infty$

$g(x)\rightarrow 0\text{ as }x\rightarrow \infty$

Therefore, the function have common horizontal asymptote, i.e., y=0.