9514 1404 393
Answer:
- asymptotes: x = ±5; y = 0
- zero: x = 0
Step-by-step 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.
