SOLUTION: Suppose that f(x)= (5x) _________ (x^2)−x−6 (that is supposed to be fraction form- did it like that to prevent confusion) a. Determine the domain of f

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Question 889563: Suppose that f(x)=
(5x)
_________
(x^2)−x−6
(that is supposed to be fraction form- did it like that to prevent confusion)
a. Determine the domain of f
b. Determine the vertical asymptote(s), if any, of the graph of f
c. Determine the horizontal asymptote(s), if any, of the graph of f
d, Sketch the graph of f
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=(5x)/(x^2-x-6)

Should render with the triple brace tags as f%28x%29=%285x%29%2F%28x%5E2-x-6%29

There is an x-axis intercept at x=0.
f%28x%29=%285x%29%2F%28%28x%2B2%29%28x-3%29%29
Vertical asymptotes are at x=-2 and x=3, at which f is undefined.
Domain is -infinity%3Cx%3C-2 and -2%3Cx%3C3 and 3%3Cx%3Cinfinity.
f approaches 0 as x tends to negative or positive infinity, so the horizontal asymptote is y=0.

graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C%285x%29%2F%28x%5E2-x-6%29%29

to show horizontal asymptote location better,
graph%28300%2C300%2C-20%2C20%2C-20%2C20%2C%285x%29%2F%28x%5E2-x-6%29%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+5x%2F%28x%5E2-x-6%29
f%28x%29=+5x%2F%28x-3%29%28x%2B2%29%29
a. Determine the domain of f
all real numbers except x≠3 or x≠-2
(-∞,-2) U (-2, 3) U (3,∞)
..
b. Determine the vertical asymptote(s), if any, of the graph of f
x=3 and x=-2
..
c. Determine the horizontal asymptote(s), if any, of the graph of f
y=0 or x-axis
..
number line:
<....-...-2...+...0...-...3..+...>
..
d, Sketch the graph of f
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%285x%29%2F%28x%5E2-x-6%29%29