Question

What is the graph to the rational function?

Answer 1

We are given

`y=(x^2-4x+3)/(x^2-9)`

Vertical asymptotes:

Firstly, we will factor numerator and denominator

we get

`y=((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=(1)/(1)`

`y=1`

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