Question

Show all work to identify the asymptotes and zero of the function f(x)=3x/x^2-9

Answer 1

steps below

Explanation:

f(x) = 3x / (x² - 9) = 3x / (x+3)(x-3)

vertical asymptotes: when denominator = 0

x = 3 and x = -3 ..... vertical asymptotes

the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.

y=0 .... horizontal asymptote

f(x) = 0 = 3x / (x² - 9) (x² - 9)≠0

3x = 0 x = 0 ......zero (roots)