Question

Which graph represents the function of f(x) = 4x^2-16/2x-4

Answer 1

Answer:

The graph in the attachment.

Step-by-step explanation:

$f(x)=\dfrac{4x^2-16}{2x-4}=\dfrac{2^2x^2-4^2}{2x-4}=\dfrac{(2x)^2-4^2}{2x-4}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\f(x)=\dfrac{(2x-4)(2x+4)}{2x-4}\\\\DOMAIN:\\\\2x-4\neq0\qquad\text{add 4 to both sides}\\\\2x\neq4\qquad\text{divide both sides by 2}\\\\x\neq2\\----------------------\\\text{We can simplify the expression. Cancel (2x-4)}\\\\y=2x+4\leftarrow\text{it's a linear function.}$

$\text{Draw the line with o}\text{pen circle for x = 2.}\\\\\text{We need only two points to plot the graph of the linear function.}\\\\\text{Choice any two value of x except 2. Put into the equation of y}\\\text{and calculate the values of y:}\\\\for\ x=0\to y=2(0)+4=0+4=4\to(0,\ 4)\\for\ x=1\to y=2(1)+4=2+4=6\to(1,\ 6)$