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

we know that

the expression represent the function

$f(x)=\frac{4x^2-4x-8}{2x+2}$

Factor $4$ in the numerator

Factor $2$ in the denominator

so

$f(x)=\frac{4(x^2-x-2)}{2(x+1)}$

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

Simplify the function

$f(x)=\frac{4(x^2-x-2)}{2(x+1)}=\frac{4(x+1)(x-2)}{2(x+1)}$

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

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

Answer 2

Answer:

Step-by-step explanation:

we know that

the expression represent the function

Factor  in the numerator

Factor  in the denominator

so

the domain of the function is all real numbers except for  because the denominator can not be zero

Simplify the function

Remember that for  the function does not exist

so

find the value of f(x) for  in the simplified function

The function has a discontinuity at point  

therefore

the answer is the option

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