Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Functions
Section9.1: Relations And Functions
Problem 75PS
Related questions
Question
How would I go about solving 13 and 14?
![### Algebra - Piecewise and Symmetric Functions
#### Problems:
**12)** \( f(x) = -x^2 - 2x \)
**Evaluate the piecewise function at the given value of the independent variable.**
**13)**
\[
f(x) =
\begin{cases}
-3x - 1 & \text{if } x < 0 \\
-4x - 2 & \text{if } x \geq 0
\end{cases}
\]
Evaluate \( f(3) \):
**Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd.**
**14)**
 *(The graph is included in the original document.)*
#### Explanation of the Graph (Problem 14):
The graph provided is plotted on a coordinate plane with the x-axis and y-axis marked at intervals of 1 unit. The curve depicted passes through various points and exhibits certain symmetry.
The y-values for corresponding points on either side of the y-axis are:
- At \( x = -3 \), \( y = -2 \)
- At \( x = -2 \), \( y = 3 \)
- At \( x = -1 \), \( y = 6 \)
- At \( x = 0 \), \( y = 5 \)
- At \( x = 1 \), \( y = 2 \)
- At \( x = 2 \), \( y = -3 \)
- At \( x = 3 \), \( y = -6 \)
The curve appears to be symmetric with respect to the y-axis, suggesting it might be an even function.
**Key Points to Identify Function Symmetry:**
- **Even Function:** Symmetric about the y-axis. For all \( x \) in the domain, \( f(x) = f(-x) \).
- **Odd Function:** Symmetric about the origin. For all \( x \) in the domain, \( f(x) = -f(-x) \).
- **Neither:** If the function does not satisfy either of the above conditions.
A detailed analysis of the graph would help determine the symmetry and the nature of the function depicted.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F23e1a652-f0bf-48f4-b702-909919a37d9c%2F984f925b-8e33-4975-8d0e-08fc31915d5b%2Fedsefl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Algebra - Piecewise and Symmetric Functions
#### Problems:
**12)** \( f(x) = -x^2 - 2x \)
**Evaluate the piecewise function at the given value of the independent variable.**
**13)**
\[
f(x) =
\begin{cases}
-3x - 1 & \text{if } x < 0 \\
-4x - 2 & \text{if } x \geq 0
\end{cases}
\]
Evaluate \( f(3) \):
**Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd.**
**14)**
 *(The graph is included in the original document.)*
#### Explanation of the Graph (Problem 14):
The graph provided is plotted on a coordinate plane with the x-axis and y-axis marked at intervals of 1 unit. The curve depicted passes through various points and exhibits certain symmetry.
The y-values for corresponding points on either side of the y-axis are:
- At \( x = -3 \), \( y = -2 \)
- At \( x = -2 \), \( y = 3 \)
- At \( x = -1 \), \( y = 6 \)
- At \( x = 0 \), \( y = 5 \)
- At \( x = 1 \), \( y = 2 \)
- At \( x = 2 \), \( y = -3 \)
- At \( x = 3 \), \( y = -6 \)
The curve appears to be symmetric with respect to the y-axis, suggesting it might be an even function.
**Key Points to Identify Function Symmetry:**
- **Even Function:** Symmetric about the y-axis. For all \( x \) in the domain, \( f(x) = f(-x) \).
- **Odd Function:** Symmetric about the origin. For all \( x \) in the domain, \( f(x) = -f(-x) \).
- **Neither:** If the function does not satisfy either of the above conditions.
A detailed analysis of the graph would help determine the symmetry and the nature of the function depicted.
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