Question

Show all work to identify the asymptotes and zero of the function f(x) = 3 x over quantity x squared minus 9.

Answer 1

Answer:

Discontinuity: x = -3 and x = 3

Zero: x = 0

Step-by-step explanation:

We know that a function is discontinuous, when the denominator of the function is 0. So let's see what the denominator equals.

x2 - 9 = 0

    +9 = +9

x2 = 9

x = + 3

Now lets find the zeros of the function by substituting y = 0 in the function.

0 = 3x/(x2 - 9)  (x2 - 9)

0 = 3x

0/3 = 3x/3

0 = x

This means that the function is discontinuous at points x = -3 and x = 3. the zero of the function x = 0.