9514 1404 393
Answer:
- asymptotes: x = ±4, y = 0
- zero: x = 0
Step-by-step explanation:
The function factors as ...
[tex]f(x)=\dfrac{4x}{(x-4)(x+4)}[/tex]
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
