Question

Which function has the following characteristics?

A vertical asymptote at x = 3
A horizontal asymptote y = 2
Domain: {x =/ +-3} (plus and minus 3)

A. y= (2x-8)/(x-3)
B. y=(x^2-9)/(x^2-4)
C. y= (2x^2-18)/(x^2-4)
D. y= (2x^2-8)/(x^2-9)

Im thinking it's either A. or D. just not sure?

Please help and explain. Thank you!

Answer 1

for the vertical asymptote

look for a function where x = 3 will result in the denominator being zero.

horizontal asymptote, means the degree of numerator and denominator are the same. But the numerator has a coefficient of the leading term that is double the coefficient of the leading term in the denominator..

hope it helps

Answer 2

the other thing you can do to help you decide between A and D is to graph them using

https://www.desmos.com/calculator

it should help you identify the correct solution

Answer 3

remember that D is the difference of 2 squares....

\[x^2 - 9 = (x - 3)(x + 3)\]

so how many vertical asymptotes...and where are they

Answer 4

thank you for your time. earlier you said to look for the vertical asymptote function where x = 3 that would be A.

Answer 5

well the vertical asymptote occurs when x = 3 it makes the denominator zero... but D is a quadratic denominator... so will have 2 values.... x = 3 and x = -3... as vertical asymptotes...

my choice would be A

Answer 6

I was thinking A. I also see that D. has the Domain: {x =/ +-3}?

Answer 7

that's a valid point about the domain of so I'd say D