The rational function presented in the image is:

$f(x) = \frac{2x - 1}{-x + 2}$

To graph this function, we need to identify key features such as vertical and horizontal asymptotes, and plot a few points. Here's the step-by-step process:

Step 1: Find the Vertical Asymptote

The vertical asymptote occurs where the denominator is zero (since division by zero is undefined). Setting the denominator equal to zero:

$-x + 2 = 0 \implies x = 2$

Thus, there is a vertical asymptote at $x = 2$.

Step 2: Find the Horizontal Asymptote

To find the horizontal asymptote, compare the degrees of the numerator and denominator. Both the numerator and the denominator are first-degree polynomials. The horizontal asymptote is determined by the ratio of the leading coefficients:

$\frac{2}{-1} = -2$

Therefore, the horizontal asymptote is $y = -2$.

Step 3: Plot Points

To better understand the graph, we can find a few points by substituting values for $x$:

1. For $x = 0$: $f(0) = \frac{2(0) - 1}{-(0) + 2} = \frac{-1}{2} = -\frac{1}{2}$ So, the point ( (0, -\frac{1}{2