Question

Show all work to identify the asymptotes and zero of the function f of x equals 4 x over quantity x squared minus 16.

Answer 1

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Answer:

• asymptotes: x = ±4, y = 0
• zero: x = 0

Step-by-step explanation:

The function factors as ...

  $f(x)=\dfrac{4x}{(x-4)(x+4)}$

The vertical asymptotes are found where the denominator factors are zero:

  x-4 = 0   ⇒   x = 4

  x+4 = 0   ⇒   x = -4

The zero of the function is where the numerator is zero:

  4x = 0   ⇒   x = 0

The horizontal asymptote of the function is the value of 4x/x² when x tends to infinity. That value is zero. The equation of the horizontal asymptote is ...

  y = 0