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Evaluate the piecewise function at the given value of the independent variable. 13) f(x) = -3x-1 ifx<0 f(3) 1-4x-2 if x20

Evaluate the piecewise function at the given value of the independent variable. 13) f(x) = -3x-1 ifx<0 f(3) 1-4x-2 if x20

Intermediate Algebra
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
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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)** ![Graph](graph_image_url) *(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.
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)** ![Graph](graph_image_url) *(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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