Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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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 \](https://content.bartleby.com/qna-images/question/bae73a37-719e-4892-8745-1f816a181ea7/7a2379b1-dfd3-49d4-b7fb-963cbb12ca10/ii57gmt_processed.jpeg)
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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