https://file.aiquickdraw.com/mathbot/file/1726811597978qy2tjur9.jpg

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

Trazar el gráfico de la función racional: f(x) = (2x - 1)/(-x + 2)

Learn how to graph the rational function f(x) = (2x - 1)/(-x + 2). This solution explains how to find the vertical asymptote at x = 2 and the horizontal asymptote at y = -2, and includes step-by-step graphing instructions. Suitable for high school students in Grades 10-12.

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