SOLUTION: I could use some help on this one. I really appreciate it! Let f(x) = 6x^2 - 24 / x^2 - 36 (a) State the y-intercept. (b) State the x-intercept(s). (c) State the v

Question 1039074: I could use some help on this one. I really appreciate it!
Let f(x) = 6x^2 - 24 / x^2 - 36
(a) State the y-intercept.

(b) State the x-intercept(s).

(c) State the vertical asymptote(s).

(d) State the horizontal asymptote.
Thank you so much for your help!

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let f(x) = 6x^2 - 24 / x^2 - 36
(a) State the y-intercept.
Let x = 0, then
f(0) = -24/-36 = 2/3 ; (that is the y-intercept)
--------------------------
(b) State the x-intercept(s).
Let y = 0, then
(6x^2-24)/(x^2-36) = 0
6x^2 - 24 = 0
6(x^2-4) = 0
x^2-4 = 0
x = 2 or x = -2
------------------------
(c) State the vertical asymptote(s).
Solve x^2-36 = 0
(x-6)(x+6) = 0
x = 6 or x = -6
Those are the VA's
--------------------------
(d) State the horizontal asymptote.
y = 6x^2/x^2 = 6
That is the HA.
Cheers,
Stan H.
RELATED QUESTIONS
I would really appreciate assistance on the following problem: I have a graph with the (answered by stanbon)

I really need help w/ this problem. Anything is appreciated! Let P(x)= -.25x^4 +... (answered by solver91311)

I could use some help on this problem, anything is helpful! f(x) = 6x − 2... (answered by Boreal)

I'm a little fuzzy on this question and could use some expertise: Let f(x) = 7x^2 + 5... (answered by stanbon)

Good evening, i need some help. it's due this morning thanks. Using the function, g(x)=... (answered by josgarithmetic)

for the function f defined by f(x)=4x^2+5x+9, find the following values: a. f(-2)= b.... (answered by math-vortex)

(8 pts) Let f(x)=(5x^2-20)/(x^2-16). (no explanations required) (a) State the... (answered by mathsolverplus)

Hello, I am stuck on a problem and I need some help please. The problem is the... (answered by Alan3354)

Hi there, I was doing my Advanced functions homework and have been stuck with this... (answered by jim_thompson5910)