Question

Show all work to identify the asymptotes and zero of the faction f(x) = 4x/x^2 - 16.

Answer 1

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