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

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.

9 x 8 divided by (5-3)=36