Question

Which graph represents the function of f(x) = the quantity of 4 x squared minus 16, all over 2 x minus 4?

Answer 1

Just translate from English to Math language:

f(x) = (4x²-16) / (2x - 4) which can be written f(x) = (2x-4)(2x+4) / (2x - 4)

Simplify by (2x-4) ==> f(x) = 2x + 4, which is linear function intersecting y-axis at y=4 & the x-axis at x= - 2 

Answer 2

Answer:

We are given with a function , $f(x)=\frac{4x^2-16}{2x-4}$

To find graph for the f(x).

First we simplify the given function.

Consider,

$f(x)=\frac{4x^2-16}{2x-4}$

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

using identity, a² - b² = ( a - b )( a + b )

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

f(x) = 2x + 4

Obtained function represent a straight line whose slope is 2 and y-intercept is 4

Let say, y = 2x + 4

then when x = 0 we get, y = 4

when y = 0 we get, x = -2

So we get a graph of function that is a line passing through ( 0 , 4 )  and

( -2 , 0 )