**Graphing Linear Functions** **Function and Inverse Function:** - **Function:** \( f(x) = 3x - 1 \) On this worksheet, you are tasked with graphing the linear function \( f(x) = 3x - 1 \) along with its inverse, \( f^{-1}(x) \). **Graph Details:** - The graph provided is a standard Cartesian plane with x and y axes. - The grid consists of squares, each representing a unit measure, to facilitate easy plotting. **Steps for Graphing:** 1. **Plot the Function \( f(x) = 3x - 1 \):** - Find the y-intercept at \( x = 0 \), which is \( y = -1 \). - Use the slope (3) to determine other points (for every increase of 1 in \( x \), \( y \) increases by 3). 2. **Find the Inverse Function \( f^{-1}(x) \):** - Assume \( y = f(x) \), so \( y = 3x - 1 \). - Solve for \( x \): \[ y = 3x - 1 \\ y + 1 = 3x \\ x = \frac{y + 1}{3} \] - This gives \( f^{-1}(x) = \frac{x + 1}{3} \). 3. **Plot the Inverse Function:** - Find the y-intercept at \( x = 0 \), which is \( y = \frac{1}{3} \). - Use the slope (1/3) to determine other points (for every increase of 3 in \( x \), \( y \) increases by 1). By successfully plotting both the function and its inverse on the graph, you have completed the exercise of understanding and visualizing linear functions and their inverses. **Additional Notes:** - Ensure to label the axes and the functions clearly. - Check your points by choosing values of \( x \), calculating \( y \), and verifying their positions on the graph.
**Graphing Linear Functions** **Function and Inverse Function:** - **Function:** \( f(x) = 3x - 1 \) On this worksheet, you are tasked with graphing the linear function \( f(x) = 3x - 1 \) along with its inverse, \( f^{-1}(x) \). **Graph Details:** - The graph provided is a standard Cartesian plane with x and y axes. - The grid consists of squares, each representing a unit measure, to facilitate easy plotting. **Steps for Graphing:** 1. **Plot the Function \( f(x) = 3x - 1 \):** - Find the y-intercept at \( x = 0 \), which is \( y = -1 \). - Use the slope (3) to determine other points (for every increase of 1 in \( x \), \( y \) increases by 3). 2. **Find the Inverse Function \( f^{-1}(x) \):** - Assume \( y = f(x) \), so \( y = 3x - 1 \). - Solve for \( x \): \[ y = 3x - 1 \\ y + 1 = 3x \\ x = \frac{y + 1}{3} \] - This gives \( f^{-1}(x) = \frac{x + 1}{3} \). 3. **Plot the Inverse Function:** - Find the y-intercept at \( x = 0 \), which is \( y = \frac{1}{3} \). - Use the slope (1/3) to determine other points (for every increase of 3 in \( x \), \( y \) increases by 1). By successfully plotting both the function and its inverse on the graph, you have completed the exercise of understanding and visualizing linear functions and their inverses. **Additional Notes:** - Ensure to label the axes and the functions clearly. - Check your points by choosing values of \( x \), calculating \( y \), and verifying their positions on the graph.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Graphing Linear Functions**
**Function and Inverse Function:**
- **Function:** \( f(x) = 3x - 1 \)
On this worksheet, you are tasked with graphing the linear function \( f(x) = 3x - 1 \) along with its inverse, \( f^{-1}(x) \).
**Graph Details:**
- The graph provided is a standard Cartesian plane with x and y axes.
- The grid consists of squares, each representing a unit measure, to facilitate easy plotting.
**Steps for Graphing:**
1. **Plot the Function \( f(x) = 3x - 1 \):**
- Find the y-intercept at \( x = 0 \), which is \( y = -1 \).
- Use the slope (3) to determine other points (for every increase of 1 in \( x \), \( y \) increases by 3).
2. **Find the Inverse Function \( f^{-1}(x) \):**
- Assume \( y = f(x) \), so \( y = 3x - 1 \).
- Solve for \( x \):
\[
y = 3x - 1 \\
y + 1 = 3x \\
x = \frac{y + 1}{3}
\]
- This gives \( f^{-1}(x) = \frac{x + 1}{3} \).
3. **Plot the Inverse Function:**
- Find the y-intercept at \( x = 0 \), which is \( y = \frac{1}{3} \).
- Use the slope (1/3) to determine other points (for every increase of 3 in \( x \), \( y \) increases by 1).
By successfully plotting both the function and its inverse on the graph, you have completed the exercise of understanding and visualizing linear functions and their inverses.
**Additional Notes:**
- Ensure to label the axes and the functions clearly.
- Check your points by choosing values of \( x \), calculating \( y \), and verifying their positions on the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3a3de44-cb4e-408a-b59e-d18e349b6cf3%2F5729ee19-3a77-4501-bf92-efa1364b0706%2Fy4fican.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing Linear Functions**
**Function and Inverse Function:**
- **Function:** \( f(x) = 3x - 1 \)
On this worksheet, you are tasked with graphing the linear function \( f(x) = 3x - 1 \) along with its inverse, \( f^{-1}(x) \).
**Graph Details:**
- The graph provided is a standard Cartesian plane with x and y axes.
- The grid consists of squares, each representing a unit measure, to facilitate easy plotting.
**Steps for Graphing:**
1. **Plot the Function \( f(x) = 3x - 1 \):**
- Find the y-intercept at \( x = 0 \), which is \( y = -1 \).
- Use the slope (3) to determine other points (for every increase of 1 in \( x \), \( y \) increases by 3).
2. **Find the Inverse Function \( f^{-1}(x) \):**
- Assume \( y = f(x) \), so \( y = 3x - 1 \).
- Solve for \( x \):
\[
y = 3x - 1 \\
y + 1 = 3x \\
x = \frac{y + 1}{3}
\]
- This gives \( f^{-1}(x) = \frac{x + 1}{3} \).
3. **Plot the Inverse Function:**
- Find the y-intercept at \( x = 0 \), which is \( y = \frac{1}{3} \).
- Use the slope (1/3) to determine other points (for every increase of 3 in \( x \), \( y \) increases by 1).
By successfully plotting both the function and its inverse on the graph, you have completed the exercise of understanding and visualizing linear functions and their inverses.
**Additional Notes:**
- Ensure to label the axes and the functions clearly.
- Check your points by choosing values of \( x \), calculating \( y \), and verifying their positions on the graph.
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