Question 546688
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, ∞)
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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