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.

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Answered: Evaluate the piecewise function at the…

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

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...

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