Answer:
Vertical asymptote: x=2
Horizontal asymptote: y=5
Step-by-step explanation:
Hi there!
The parent function for a rational function has a horizontal asymptote at y=0 and a vertical asymptote at x=0.
First, we want to perform long division on 5x/x-2. Please check the image attached.
The result is [tex]5+\displaystyle\frac{10}{x-2}[/tex].
Here are the transformations of a rational function:
[tex]f(x)=\displaystyle\frac{a}{b(x-h)}+k[/tex]
a = vertical stretch
b = horizontal stretch
h = horizontal translation
k = vertical translation
Stretches don't change the location of the asymptotes, only the translations do.
According to [tex]5+\displaystyle\frac{10}{x-2}[/tex], we applied a horizontal translation of 2 units right and a vertical translation of 5 units up. Therefore, our asymptotes are now x=2 and y=5.
I hope this helps!
