Answer:
- asymptotes: x = -5, x = 5
- zero: x = 0
Step-by-step explanation:
The function of interest is ...
[tex]f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}[/tex]
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
__
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.
