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Show all work to identify the asymptotes and zero of the function f(x)=5x (over) x^2-25

Show all work to identify the asymptotes and zero of the function f(x)=5x (over) x-example-1
User Macarthy
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Answer:

  • asymptotes: x = ±5; y = 0
  • zero: x = 0

Explanation:

The function will have a zero where the numerator is zero:

5x = 0

x = 0 . . . . divide by 5

The zero of the function is x=0.

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The function will have vertical asymptotes where the denominator is zero:

x^2 -25 = 0

x^2 = 25 . . . . add 25

x = ±5 . . . . . . take the square root

The function will have vertical asymptotes at x = -5 and x = 5.

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When x gets large, the magnitude of the function is approximately ...

5x/x^2 = 5/x

As x approaches infinity, this value approaches zero.

The function will have a horizontal asymptote at y = 0.

Show all work to identify the asymptotes and zero of the function f(x)=5x (over) x-example-1
User CJ Gaconnet
by
7.8k points

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