Question 546688: Given the rational function: f(x)=7x / x^2-16
Find
a. The domain
b. All intercepts
c. All asymptotes
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Given the rational function: f(x)=7x / x^2-16
Find
a. The domain
When checking domain look for terms with sqrt and zeros in the denominator which would make function undefined. Since there are no sqrts in given equation, check for zeros in the denominator.
x^2-16=0
(x+4)(x-4)=0
x=-4 and x=4
domain:{x|x≠-4, x≠4}, or (-∞,-4) U (-4, 4) U (4, ∞)
..
b. All intercepts
x-intercepts, set y=0, then solve for x
7x / x^2-16=0
7x=0
x=0 (x-intercept)
..
y-intercepts, set x=0, then solve for y
f(0)=7x / x^2-16=0 (y-intercept)
..
c. All asymptotes, set denominator=zero, then solve for x
x^2-16=0
(x+4)(x-4)=0
x=-4 and x=4
asymptotes are x=-4 and x=4
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