Question

Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25.

Answer 1

Answer:

• asymptotes: x = -5, x = 5
• zero: x = 0

Step-by-step explanation:

The function of interest is ...

  $f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}$

The asymptotes are found where the denominator is zero. It will be zero when either factor is zero, so at x = 5 and x = -5

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The zeros are found where the numerator is zero. It will be zero for x = 0.

The asymptotes are x=-5, x=5; the zero is x=0.