Question

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

Answer 1

Answer:

D edge2020

Step-by-step explanation:

Answer 2

ANSWER

The last graph is the correct answer

EXPLANATION

The function,
$y = \frac{3x - 2}{x - 2}$ 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,

$y = \frac{3}{1}$

Thus, the horizontal asymptote occurs at
$y = 3$

At x-intercept,
$f(x) = 0$

This implies that,

$\frac{3x - 2}{x - 2} = 0$

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

$3x = 2$

$\Rightarrow \: x = \frac{2}{3}$

The graph cuts the x-axis at,

$( \frac{2}{3} ,0)$

At y-intercept,

$x = 0$

This implies that,

$f(0) = \frac{3(0) - 2}{0 - 2} = \frac{ - 2}{ - 2} = 1$

The graph cuts the y-axis at,

$(0,1)$

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