Answer:
Step-by-step explanation:
[tex]f(x) = \frac{4x^2 - 16} {2x - 4} \\\\[/tex]
[tex]=\frac{4(x^2 -4)}{2(x-2)}\\\\=\frac{2 (x^2 - 2^2)}{(x-2)}\\\\=\frac{2(x+2)(x-2)}{(x-2)}\\\\=\frac{2(x+2)}{1}\\\\=2(x+2)\\\\=2x + 4[/tex]
Graph is a straight line ( -2 , 0) and ( 0 , 4 )
The function represents a straight line graph with slope =2 and intercept = 4.
A function is a law that relates a dependent and an independent variable.
The function given is
[tex]\rm f(x) = \dfrac{ 4x^2 -16}{2x-4}\\\\[/tex]
This function can be simplified as
[tex]\rm f(x) = \dfrac{ 4(x^2 -4)}{2(x-2)}\\\\\\f(x) = \dfrac{ 4(x+2)(x-2)}{2(x-2)}\\\\\\[/tex]
f(x)= 2 (x+2)
y = 2x +4
Therefore the function represents a straight line graph with slope =2 and intercept = 4.
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