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Graph the rational function. 6 ƒ(x)=-2x-1 Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the

Graph the rational function. 6 ƒ(x)=-2x-1 Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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## Graphing Rational Functions **Objective:** To graph the rational function: \[ f(x) = \frac{-6}{-2x - 1} \] ### Instructions 1. **Identify and Draw Asymptotes:** - **Vertical Asymptote:** This occurs where the denominator equals zero. \[ -2x - 1 = 0 \rightarrow x = -\frac{1}{2} \] - **Horizontal Asymptote:** For rational functions of the form \( \frac{a}{bx + c} \), the horizontal asymptote is \( y = 0 \). 2. **Plot Points:** - Choose values for \( x \) to find corresponding \( y \) values and plot at least two points on each piece of the graph. ### Tools Provided - **Graph Area:** A coordinate plane labeled with \( x \) and \( y \) axes. - **Drawing Tools:** - Pencil icon for drawing. - A "Curve" tool for plotting curve pieces. - Eraser tool for corrections. - Reset button to start over. ### Graph Description - The coordinate plane includes \( x \) and \( y \) axes ranging from -8 to 8 (on both axes). - The grid is helpful for accurate plotting of points and drawing of asymptotes. ### Interactive Steps 1. **Draw Asymptotes:** - Use the pencil tool to draw the vertical asymptote at \( x = -\frac{1}{2} \). - Draw the horizontal asymptote at \( y = 0 \). 2. **Plot Points:** - Plot points by selecting key values of \( x \) (e.g., \( x = -1 \) and \( x = 1 \)) and computing \( f(x) \). 3. **Connect Points:** - Use the curve tool to draw the graph of the function, approaching the asymptotes as necessary. ### Example of Point Calculation - For \( x = -1 \): \[ f(-1) = \frac{-6}{-2(-1) - 1} = \frac{-6}{2 - 1} = -6 \] Thus, plot the point \((-1, -6)\). - For \( x = 1 \
Transcribed Image Text:## Graphing Rational Functions **Objective:** To graph the rational function: \[ f(x) = \frac{-6}{-2x - 1} \] ### Instructions 1. **Identify and Draw Asymptotes:** - **Vertical Asymptote:** This occurs where the denominator equals zero. \[ -2x - 1 = 0 \rightarrow x = -\frac{1}{2} \] - **Horizontal Asymptote:** For rational functions of the form \( \frac{a}{bx + c} \), the horizontal asymptote is \( y = 0 \). 2. **Plot Points:** - Choose values for \( x \) to find corresponding \( y \) values and plot at least two points on each piece of the graph. ### Tools Provided - **Graph Area:** A coordinate plane labeled with \( x \) and \( y \) axes. - **Drawing Tools:** - Pencil icon for drawing. - A "Curve" tool for plotting curve pieces. - Eraser tool for corrections. - Reset button to start over. ### Graph Description - The coordinate plane includes \( x \) and \( y \) axes ranging from -8 to 8 (on both axes). - The grid is helpful for accurate plotting of points and drawing of asymptotes. ### Interactive Steps 1. **Draw Asymptotes:** - Use the pencil tool to draw the vertical asymptote at \( x = -\frac{1}{2} \). - Draw the horizontal asymptote at \( y = 0 \). 2. **Plot Points:** - Plot points by selecting key values of \( x \) (e.g., \( x = -1 \) and \( x = 1 \)) and computing \( f(x) \). 3. **Connect Points:** - Use the curve tool to draw the graph of the function, approaching the asymptotes as necessary. ### Example of Point Calculation - For \( x = -1 \): \[ f(-1) = \frac{-6}{-2(-1) - 1} = \frac{-6}{2 - 1} = -6 \] Thus, plot the point \((-1, -6)\). - For \( x = 1 \
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