Question

Identify the discontinuities, graph, and find the zeros of the rational function
f(x) =(x^2-100)/(x+10)

Answer 1

the discontinuity will occur when the denominator, (x+10)=0
factored form of f(x) is (x-10)(x+10)/(x+10)
x+10=0
x=-10
The graph is discontinuous at x=-10. this is a removable, or point, discontinuity because (x+10) is a factor of the numerator.
The zeros of the rational function occur when the numerator equals 0:
(x+10)(x-10)=0
x=10, -10

Answer 2

however, because the function is not defined at x=-10, there is only 1 zero for this function. that is x=10