Question

Which graph represents the function of f(x) = the quantity of 4 x squared minus 4 x minus 8, all over 2 x plus 2?

graph of 2 x minus 4, with discontinuity at negative 1, negative 6
graph of 2 x minus 4, with discontinuity at 1, negative 2
graph of 2 x plus 2, with discontinuity at negative 1, 0
graph of 2 x plus 2, with discontinuity at 1, 4

its not b. PLEASE SOMEONE HELP ME THANK YOU!!

Answer 1

Answer: D: 2 x minus 4, with discontinuity at negative 1, negative 6

Explanation:

Answer 2

we know that

the expression represent the function

`f(x)=(4x^2-4x-8)/(2x+2)`

Factor
`4` in the numerator

Factor
`2` in the denominator

so

`f(x)=(4(x^2-x-2))/(2(x+1))`

the domain of the function is all real numbers except for
`x=-1` because the denominator can not be zero

Simplify the function

`f(x)=(4(x^2-x-2))/(2(x+1))=(4(x+1)(x-2))/(2(x+1))`

`f(x)=2(x-2)=2x-4`

Remember that for
`x=-1` the function does not exist

so

find the value of f(x) for
`x=-1` in the simplified function

`f(x)=2x-4`

`f(-1)=2*(-1)-4=-6`

The function has a discontinuity at point
`(-1,-6)`

therefore

the answer is the option

graph of 2 x minus 4, with discontinuity at negative 1, negative 6