Show all work to identify the discontinuity and zero of the function f of x equals 6 x over quantity x squared minus 36.

discontinuity: x = - 6, x = 6 zero: x = 0

Step-by-step explanation:

The denominator of the function can be factored using the form for the difference of squares:

a² - b² = (a - b) (a + b)

f (x) = 6x / (x² - 36) = 6x / (x² - 6²)

f (x) = 6x / ((x - 6) (x + 6))

There will be discontinuities where the denominator factors are zero, at x = ±6. There will be a zero where the numerator factor is zero, at x = 0.