Question

What is the graph to the rational function?

Answer 1

We are given

$y=\frac{x^2-4x+3}{x^2-9}$

Vertical asymptotes:

Firstly, we will factor numerator and denominator

we get

$y=\frac{(x-1)(x-3)}{(x-3)(x+3)}$

We can see that (x-3) is common in both numerator and denominator

so, we will only set x+3 to 0

and then we can find vertical asymptote

$x+3=0$

$x=-3$

Hole:

We can see that (x-3) is common in both numerator and denominator

so, hole will be at x-3=0

$x-3=0$

$x=3$

Horizontal asymptote:

We can see that degree of numerator is 2

degree of denominator is also 2

for finding horizontal asymptote, we find ratio of leading coefficients of numerator and denominator

and we get

$y=\frac{1}{1}$

$y=1$

so, option-D............Answer