Question

What are the coordinates of the hole in the graph of the function f(x)?

Answer 1

Answer:

The coordinates are (2,8)

Step-by-step explanation:

A hole is where both the numerator and the denominator are zero

f(x)=x^2+4x−12 / x−2

Factor the numerator

f(x) = (x+6) (x-2)/ (x-2)

The hole will occur where x-2 =0

x-2=0

Add 2 to each side

x-2+2 =0+2

x=2

There is a hole at x=2

If we could cancel the x-2 values from the top and bottom, we are left with

f(x) = x+6

At x=2

f(2) = 6+2

f(2) would be 8

The coordinates are (2,8)

There is a hole