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,...
Related questions
Question
#28
![**Transcription for Educational Website**
**27.** Use a translation to graph the equation. Please describe how:
\[ f(x) = |x - 5| + 2 \]
- Absolute value function
- Translated 5 units to the right and 2 units up
**Graph Description:**
The graph shows a V-shaped absolute value function. It is translated from the origin 5 units to the right and 2 units up, as indicated by the arrows on the graph with labels "→5 ↑2".
**28.** Use \( f(x) = \sqrt{x} \) to translate the following two functions:
a. \[ g(x) = 5\sqrt{x + 2} \]
b. \[ g(x) = \frac{1}{5}\sqrt{x - 2} \]
Both functions involve horizontal shifts: left for (a) by 2, right for (b) by 2, and vertical stretching/compression factors.
**Diagram Explanation:**
The diagram shows transformations of the square root function. They appear as curves starting from the x-axis, showing translation and possible stretching/compression.
**29.** The graph of the function \( f(x) \) is a reflection of the graph of:
\[ f(x) = -x^3 \]
Please describe how you translate the function.
**Diagram Explanation:**
The graph would reflect the cubic function across the x-axis, showing inversion at each point of the original cubic curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d7dc8e5-26a6-47cd-a7e6-f6c748f94583%2Fb05b0c2b-c4b9-4e64-a6dc-d86bcaf3bf34%2Fwinhc8w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
**27.** Use a translation to graph the equation. Please describe how:
\[ f(x) = |x - 5| + 2 \]
- Absolute value function
- Translated 5 units to the right and 2 units up
**Graph Description:**
The graph shows a V-shaped absolute value function. It is translated from the origin 5 units to the right and 2 units up, as indicated by the arrows on the graph with labels "→5 ↑2".
**28.** Use \( f(x) = \sqrt{x} \) to translate the following two functions:
a. \[ g(x) = 5\sqrt{x + 2} \]
b. \[ g(x) = \frac{1}{5}\sqrt{x - 2} \]
Both functions involve horizontal shifts: left for (a) by 2, right for (b) by 2, and vertical stretching/compression factors.
**Diagram Explanation:**
The diagram shows transformations of the square root function. They appear as curves starting from the x-axis, showing translation and possible stretching/compression.
**29.** The graph of the function \( f(x) \) is a reflection of the graph of:
\[ f(x) = -x^3 \]
Please describe how you translate the function.
**Diagram Explanation:**
The graph would reflect the cubic function across the x-axis, showing inversion at each point of the original cubic curve.
Expert Solution
Step 1
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education