### Educational Exercise: Graphing and Inverse Reflection of Equations#### Instructions:Graph the equation by substituting and plotting points. Then, reflect the graph across the line \( y = x \) to obtain the graph of its inverse.**Given Equation:** \[ y = |x| + 6 \]#### Task:Choose the graph with the original equation as a solid line and the inverse of the equation as a dotted line.#### Options:**Option A:**- The graph features a V-shaped solid line representing \( y = |x| + 6 \), starting from the point (0, 6) and extending upwards both to the left and right.- The dotted line shows the inverse, reflected across the line \( y = x \).**Option B:**- The graph displays similar characteristics to option A, but the solid line and dotted line align differently.**Option C:**- This option also presents a V-shaped solid line and its inverse, but the alignment again differs from Option A.**Option D:**- This graph option is similar to the above but maintains consistent matching of alignment features unique to its pattern.**Ensure to carefully analyze each graph and select the correct one based on your understanding of graph reflection and inverse functions.**##### Graph Analysis:In each option, notice the geometric reflection properties and how the transformation maps the original equation across the line \( y = x \).**Note:** To view each graph more clearly, zooming in on the corresponding sections can help differentiate the details.---**Copyright © 2022 Pearson Education Inc.**All rights reserved.- [Terms of Use](#)- [Privacy Policy](#)- [Permissions](#)

We have to solve given Questions.

Graph the equation by substituting and plotting points. Then reflect the graph across the line y=x to obtain the graph of its inverse. y = |x | +6 Choose the graph with the original equation as a solid line and the inverse of the equation as a dotted line. Ο Α. O C. Ay ---- G OB. O D. Ay Q G

Graph the equation by substituting and plotting points. Then reflect the graph across the line y=x to obtain the graph of its inverse. y = |x | +6 Choose the graph with the original equation as a solid line and the inverse of the equation as a dotted line. Ο Α. O C. Ay ---- G OB. O D. Ay Q G

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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Question

### Educational Exercise: Graphing and Inverse Reflection of Equations

#### Instructions:
Graph the equation by substituting and plotting points. Then, reflect the graph across the line \( y = x \) to obtain the graph of its inverse.

**Given Equation:**
\[ y = |x| + 6 \]

#### Task:
Choose the graph with the original equation as a solid line and the inverse of the equation as a dotted line.

#### Options:

**Option A:**
- The graph features a V-shaped solid line representing \( y = |x| + 6 \), starting from the point (0, 6) and extending upwards both to the left and right.
- The dotted line shows the inverse, reflected across the line \( y = x \).

**Option B:**
- The graph displays similar characteristics to option A, but the solid line and dotted line align differently.

**Option C:**
- This option also presents a V-shaped solid line and its inverse, but the alignment again differs from Option A.

**Option D:**
- This graph option is similar to the above but maintains consistent matching of alignment features unique to its pattern.

**Ensure to carefully analyze each graph and select the correct one based on your understanding of graph reflection and inverse functions.**

##### Graph Analysis:
In each option, notice the geometric reflection properties and how the transformation maps the original equation across the line \( y = x \).

**Note:** To view each graph more clearly, zooming in on the corresponding sections can help differentiate the details.

---

**Copyright © 2022 Pearson Education Inc.**
All rights reserved.
- [Terms of Use](#)
- [Privacy Policy](#)
- [Permissions](#)

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