Homework Help is Here – Start Your Trial Now!
Math
Algebra
Evaluate f(x) at x = - 4, 2, and 4. x³-4x² if x≤-4 f(x) = 2x² x³ 3 if -4

Evaluate f(x) at x = - 4, 2, and 4. x³-4x² if x≤-4 f(x) = 2x² x³ 3 if -4

Algebra and Trigonometry (6th Edition)
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,...
See similar textbooks
icon
Related questions
Question
100%
### Evaluating Piecewise Functions Given the function \( f(x) \) defined as: \[ f(x) = \begin{cases} x^3 - 4x^2 & \text{if } x \leq -4 \\ 2x^2 & \text{if } -4 < x < 4 \\ x^3 - 48 & \text{if } x \geq 4 \end{cases} \] We are to evaluate \( f(x) \) at \( x = -4 \), \( x = 2 \), and \( x = 4 \). --- ### Evaluation Steps: 1. **Evaluate \( f(-4) \)** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( f(-4) = \) \( \boxed{\text{(Simplify your answer.)}} \) - B. The answer is undefined. 2. **Evaluate \( f(2) \)** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( f(2) = \) \( \boxed{\text{(Simplify your answer.)}} \) - B. The answer is undefined. 3. **Evaluate \( f(4) \)** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( f(4) = \) \( \boxed{\text{(Simplify your answer.)}} \) - B. The answer is undefined. --- ### Explanation of Piecewise Function - For \( x \leq -4 \), use \( f(x) = x^3 - 4x^2 \). - For \( -4 < x < 4 \), use \( f(x) = 2x^2 \). - For \( x \geq 4 \), use \( f(x) = x^3 - 48 \). Make sure to follow these rules when plugging in the values for \( x \) to determine \( f(x) \).
Transcribed Image Text:### Evaluating Piecewise Functions Given the function \( f(x) \) defined as: \[ f(x) = \begin{cases} x^3 - 4x^2 & \text{if } x \leq -4 \\ 2x^2 & \text{if } -4 < x < 4 \\ x^3 - 48 & \text{if } x \geq 4 \end{cases} \] We are to evaluate \( f(x) \) at \( x = -4 \), \( x = 2 \), and \( x = 4 \). --- ### Evaluation Steps: 1. **Evaluate \( f(-4) \)** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( f(-4) = \) \( \boxed{\text{(Simplify your answer.)}} \) - B. The answer is undefined. 2. **Evaluate \( f(2) \)** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( f(2) = \) \( \boxed{\text{(Simplify your answer.)}} \) - B. The answer is undefined. 3. **Evaluate \( f(4) \)** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. \( f(4) = \) \( \boxed{\text{(Simplify your answer.)}} \) - B. The answer is undefined. --- ### Explanation of Piecewise Function - For \( x \leq -4 \), use \( f(x) = x^3 - 4x^2 \). - For \( -4 < x < 4 \), use \( f(x) = 2x^2 \). - For \( x \geq 4 \), use \( f(x) = x^3 - 48 \). Make sure to follow these rules when plugging in the values for \( x \) to determine \( f(x) \).
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS