The graph that represents the function [tex]\mathbf{f(x) = \frac{4x^2 - 4x - 8}{2x + 2}}[/tex] is the graph of the function [tex]\mathbf{f(x) = 2x - 4}[/tex]
The function is given as:
[tex]\mathbf{f(x) = \frac{4x^2 - 4x - 8}{2x + 2}}[/tex]
Factor out 2
[tex]\mathbf{f(x) = \frac{2(2x^2 - 2x - 4)}{2(x + 1)}}[/tex]
Cancel out common factors
[tex]\mathbf{f(x) = \frac{2x^2 - 2x - 4}{x + 1}}[/tex]
Expand the numerator
[tex]\mathbf{f(x) = \frac{2x^2 -4x + 2x - 4}{x + 1}}[/tex]
Factorize
[tex]\mathbf{f(x) = \frac{2x(x -2) + 2(x - 2)}{x + 1}}[/tex]
Factor out x - 2
[tex]\mathbf{f(x) = \frac{(2x +2)(x - 2)}{x + 1}}[/tex]
Factor out 2
[tex]\mathbf{f(x) = \frac{2(x +1)(x - 2)}{x + 1}}[/tex]
Cancel out the common factors
[tex]\mathbf{f(x) = 2(x - 2)}[/tex]
Open the brackets
[tex]\mathbf{f(x) = 2x - 4}[/tex]
See attachment for the graph of [tex]\mathbf{f(x) = 2x - 4}[/tex]
Hence, the graph that represents the function [tex]\mathbf{f(x) = \frac{4x^2 - 4x - 8}{2x + 2}}[/tex] is the graph of the function [tex]\mathbf{f(x) = 2x - 4}[/tex]
Read more about graphs and functions at:
https://brainly.com/question/1880610
