Question

Alg 2; Find all holes of following function. Write answer as a coordinate point in its simplest form.

Answer 1

A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.

Factorize the numerator and denominator.

`\begin{gathered} x^2+8x-20=(x+10)(x-2) \\ 2x^2+20x=2x(x+10) \end{gathered}`

The common factor in the numerator and denominator is x+10. Equate x+10 with zero and find the value of x, which is the hole of the given function.

`\begin{gathered} x+10=0 \\ x=-10 \end{gathered}`

The function has only one hole at x = -10.