Help What is the graph???

Question

asked Sep 4, 2019 102k views

1 Answer

Apfelsaft · Answer 1 · 2019-09-10T12:59:43+0000

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

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

now, we can draw graph

Graph: