Question

Which graph represents the function of f(x) = the quantity of 4 x squared minus 4 x minus 8, all over 2 x

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
please and thank you

Answer 1

The given function is

f(x)=
`(4 x^2- 4 x -8)/(2 x)`

f(x)=
`(4 x^2)/(2 x)-(4 x)/(2x) -(8)/(2x)\\\\ = 2 x -2 -(4)/( x)`

f(x)= 2 x - 2 -
`(4)/(x)`

To find the points of Discontinuity

Put, f(x)=0

→ 2 x - 2 -
`(4)/(x)`=0

→2 x² - 2 x - 4=0×x

→2 (x²-x-2)=0

→ x² - x -2=0

Splitting the middle term

→ x² - 2 x + x -2=0

→ x×(x-2)+ 1 × (x-2)=0

→ (x+1) (x-2)=0

Gives, x= -1, and x=2.

So, the graph represented by f(x)=
`(4 x^2- 4 x -8)/(2 x)` is equal to f(x)= 2 x - 2 -
`(4)/(x)` with points of Discontinuity at -1 and 2.