Section 4.2 2. The function f is one-to-one. Find the inverse function and check your answer. Then graph f, f-¹, and the line y = x on the same coordinate axes (same graph). f(x) = 7+3x
Section 4.2 2. The function f is one-to-one. Find the inverse function and check your answer. Then graph f, f-¹, and the line y = x on the same coordinate axes (same graph). f(x) = 7+3x
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Section 4.2
2. The function \( f \) is one-to-one. Find the inverse function and check your answer. Then graph \( f \), \( f^{-1} \), and the line \( y = x \) on the same coordinate axes (same graph).
\[ f(x) = 7 + 3x \]
**Inverse function** ____________________
**Check**
**Graph**
*Description of the Graph:*
The graph is a standard coordinate plane with the x-axis labeled from \(-5\) to \(10\) and the y-axis also labeled from \(-5\) to \(10\). Each axis is marked with grid lines to facilitate accurate plotting of points. The line \( y = x \) should be plotted as a diagonal line running through the origin where x equals y, representing the standard line of reflection used when graphing functions and their inverses. The function \( f(x) = 7 + 3x \) should be plotted as a straight line based on its linear equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7685174-f9ce-4772-8265-75ce63a9919c%2F5b14020a-1b11-4982-b4d6-77af94f40ecf%2Fn64vlwd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Section 4.2
2. The function \( f \) is one-to-one. Find the inverse function and check your answer. Then graph \( f \), \( f^{-1} \), and the line \( y = x \) on the same coordinate axes (same graph).
\[ f(x) = 7 + 3x \]
**Inverse function** ____________________
**Check**
**Graph**
*Description of the Graph:*
The graph is a standard coordinate plane with the x-axis labeled from \(-5\) to \(10\) and the y-axis also labeled from \(-5\) to \(10\). Each axis is marked with grid lines to facilitate accurate plotting of points. The line \( y = x \) should be plotted as a diagonal line running through the origin where x equals y, representing the standard line of reflection used when graphing functions and their inverses. The function \( f(x) = 7 + 3x \) should be plotted as a straight line based on its linear equation.
![**Section 4.3**
**Problem 3:** Use transformations to graph the function. Determine the domain, the range, and the horizontal asymptote.
Given function:
\[ f(x) = \left(\frac{1}{3}\right)^{(x+2)} + 1 \]
**Graph Explanation:**
The graph provided is a standard Cartesian coordinate plane with labeled x-axis and y-axis. The x-axis ranges from -10 to 10, and the y-axis ranges vertically. It’s a grid with each square representing one unit.
**To Be Determined:**
- **Domain:** _________________
- **Range:** _________________
- **Horizontal Asymptote:** _________________](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7685174-f9ce-4772-8265-75ce63a9919c%2F5b14020a-1b11-4982-b4d6-77af94f40ecf%2F6sw1war_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Section 4.3**
**Problem 3:** Use transformations to graph the function. Determine the domain, the range, and the horizontal asymptote.
Given function:
\[ f(x) = \left(\frac{1}{3}\right)^{(x+2)} + 1 \]
**Graph Explanation:**
The graph provided is a standard Cartesian coordinate plane with labeled x-axis and y-axis. The x-axis ranges from -10 to 10, and the y-axis ranges vertically. It’s a grid with each square representing one unit.
**To Be Determined:**
- **Domain:** _________________
- **Range:** _________________
- **Horizontal Asymptote:** _________________
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