4. At what coordinate point with the graph of y = 3x–8 intersect that of its inverse? Explain or show how you arrived at your answer. The use of the grid below is optional.
4. At what coordinate point with the graph of y = 3x–8 intersect that of its inverse? Explain or show how you arrived at your answer. The use of the grid below is optional.
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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![### Problem 4
**Question:**
At what coordinate point does the graph of \( y = 3x - 8 \) intersect with that of its inverse? Explain or show how you arrived at your answer. The use of the grid below is optional.
**Grid Details:**
- A standard Cartesian grid is shown with horizontal (x-axis) and vertical (y-axis) lines.
- The grid is centered at the origin (0,0).
- Both axes are labeled \( x \) (horizontal) and \( y \) (vertical), with arrows indicating the positive direction.
- The grid spacing is uniform, providing an aid for calculations and sketches.
**Solution Approach:**
To find the intersection point with its inverse:
1. **Determine the Inverse Function:**
- Begin with the original equation \( y = 3x - 8 \).
- Swap \( x \) and \( y \) to find the inverse: \( x = 3y - 8 \).
- Solve for \( y \):
\[
x + 8 = 3y \quad \Rightarrow \quad y = \frac{x + 8}{3}
\]
2. **Find the Intersection Point:**
- Set the original function equal to its inverse:
\[
3x - 8 = \frac{x + 8}{3}
\]
- Clear fractions by multiplying both sides by 3:
\[
9x - 24 = x + 8
\]
- Simplify and solve for \( x \):
\[
8x = 32 \quad \Rightarrow \quad x = 4
\]
- Substitute back to find \( y \):
\[
y = 3(4) - 8 = 12 - 8 = 4
\]
3. **Conclusion:**
- The graphs intersect at the coordinate point \((4, 4)\).
This coordinate, \((4, 4)\), satisfies both the original function and its inverse, indicating their point of intersection. Using the graph can help verify these calculations by plotting both lines and confirming they meet at this point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ad25fec-b9a6-4204-b002-c754ad21ce1f%2F49036549-a30e-4872-938d-40f1525d8d9a%2Fx7cx5q3_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 4
**Question:**
At what coordinate point does the graph of \( y = 3x - 8 \) intersect with that of its inverse? Explain or show how you arrived at your answer. The use of the grid below is optional.
**Grid Details:**
- A standard Cartesian grid is shown with horizontal (x-axis) and vertical (y-axis) lines.
- The grid is centered at the origin (0,0).
- Both axes are labeled \( x \) (horizontal) and \( y \) (vertical), with arrows indicating the positive direction.
- The grid spacing is uniform, providing an aid for calculations and sketches.
**Solution Approach:**
To find the intersection point with its inverse:
1. **Determine the Inverse Function:**
- Begin with the original equation \( y = 3x - 8 \).
- Swap \( x \) and \( y \) to find the inverse: \( x = 3y - 8 \).
- Solve for \( y \):
\[
x + 8 = 3y \quad \Rightarrow \quad y = \frac{x + 8}{3}
\]
2. **Find the Intersection Point:**
- Set the original function equal to its inverse:
\[
3x - 8 = \frac{x + 8}{3}
\]
- Clear fractions by multiplying both sides by 3:
\[
9x - 24 = x + 8
\]
- Simplify and solve for \( x \):
\[
8x = 32 \quad \Rightarrow \quad x = 4
\]
- Substitute back to find \( y \):
\[
y = 3(4) - 8 = 12 - 8 = 4
\]
3. **Conclusion:**
- The graphs intersect at the coordinate point \((4, 4)\).
This coordinate, \((4, 4)\), satisfies both the original function and its inverse, indicating their point of intersection. Using the graph can help verify these calculations by plotting both lines and confirming they meet at this point.
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