which graph represents the function $f(x)=\frac{3x - 2}{x - 2}$?

Explanation:

Step1: Find the vertical asymptote

Set the denominator equal to 0. So (x - 2=0), then (x = 2).

Step2: Find the horizontal asymptote

Since the degree of the numerator and denominator are the same (both degree 1), divide the leading - coefficients. The leading coefficient of the numerator is 3 and of the denominator is 1, so (y = 3) is the horizontal asymptote.

Step3: Find the y - intercept

Set (x = 0), then (f(0)=\frac{3\times0 - 2}{0 - 2}=\frac{-2}{-2}=1).

Step4: Analyze the graph

The graph has a vertical asymptote at (x = 2), a horizontal asymptote at (y = 3) and passes through the point ((0,1)). The given graph satisfies these characteristics.

Answer:

The given graph represents the function (f(x)=\frac{3x - 2}{x - 2}).