SOLUTION: Given the rational function: f(x)=7x / x^2-16 Find a. The domain b. All intercepts c. All asymptotes

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
RELATED QUESTIONS
Find all the asymptotes, x-intercepts, and y-intercepts for the graph of the given... (answered by CubeyThePenguin,ikleyn)

Given the following rational function: (a) state the domain. (b) find the vertical... (answered by Edwin McCravy)

Consider the two functions: f(x)=x^2-4 and g(x)=2x^3-3x^2-5x+6 A. A function is defined... (answered by greenestamps)

For the given rational function f(x) = 3 - 3x over (divided by) x - 5, find the following (answered by Theo)

For the function: (x^3+2x^2-4x-8)/2x^2-8 a) Find the domain of the function, and... (answered by robertb,KMST)

Please show work Consider the function f(x)=(x^2-1)/(x-3) a Find the domain for... (answered by Boreal)

find the domain of each rational function f(x)= 7x ____________... (answered by edjones)

For the following rational equation find all the asymptotes and intercepts. Use these to... (answered by MathLover1)

Find all vertical asymptotes (if any) of the function f(x) = x/(x^2 -... (answered by rapaljer)