Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.
1 answer:
Answer:
- asymptotes: x = -4, x = 4
- zeros: x = 0
Step-by-step explanation:
The vertical asymptotes of the rational expression are the places where the denominator is zero:
x^2 -16 = 0
(x -4)(x +4) = 0 . . . . . true for x=4, x=-4
x = 4, x = -4 are the equations of the vertical asymptotes
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The zeros of a rational expression are the places where the numerator is zero:
4x = 0
x = 0 . . . . . . divide by 4
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ANSWER
Possible rational roots: <span><span>±1,±2,±3,±4,±6,±12</span><span>±1,±2,±3,±4,±6,±12</span></span>
Actual rational roots: <span><span>1,−1,2,−2,−3</span></span>
<span><span>see attachments for all steps.</span></span>