Question

Which graph represents the function f(x)=3x-2/x-2

Answer 1

D edge2020

Explanation:

Answer 2

ANSWER

The last graph is the correct answer

EXPLANATION

The function,

`y = (3x - 2)/(x - 2)` is a rational function.

This rational function has a vertical asymptote

at where the denominator is zero.

That is,

`x - 2 = 0`

This means that, the vertical asymptote occurs at


`x = 2`

The graph also has a horizontal asymptote at,


`y = (3)/(1)`

Thus, the horizontal asymptote occurs at

`y = 3`

At x-intercept,

`f(x) = 0`

This implies that,


`(3x - 2)/(x - 2) = 0`


`\Rightarrow \: 3x - 2 = 0`


`3x = 2`


`\Rightarrow \: x = (2)/(3)`

The graph cuts the x-axis at,


`( (2)/(3) ,0)`

At y-intercept,


`x = 0`

This implies that,


`f(0) = (3(0) - 2)/(0 - 2) = ( - 2)/( - 2) = 1`

The graph cuts the y-axis at,


`(0,1)`

The graph that satisfy all the above conditions is the last one.