Evaluate Piecewise Function f(x) for f(-3) + f(5)

Math Problem Statement

Homework_Relations-Functions-Their-Graphs.pdf

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You are given a piecewise function:

\begin{cases} 2x + 3 & \text{if } x < -1 \\ -x - 2 & \text{if } x \geq -1 \end{cases}$$ You are asked to find the value of $$f(-3) + f(5)$$. #### Solution: - **Step 1**: Calculate $$f(-3)$$. Since $$-3 < -1$$, we use the first part of the piecewise function $$f(x) = 2x + 3$$: $$f(-3) = 2(-3) + 3 = -6 + 3 = -3$$ - **Step 2**: Calculate $$f(5)$$. Since $$5 \geq -1$$, we use the second part of the piecewise function $$f(x) = -x - 2$$: $$f(5) = -5 - 2 = -7$$ - **Step 3**: Add the results. $$f(-3) + f(5) = -3 + (-7) = -10$$ Thus, the value of $$f(-3) + f(5)$$ is **-10**. Let me know if you want detailed explanations for other problems, or if you have any questions. Here are five related questions that can extend this topic: 1. How can you determine which part of a piecewise function to use based on the input value? 2. What are the key characteristics of piecewise functions? 3. How can we graph a piecewise function with different expressions on the same plot? 4. Can a piecewise function be continuous? If so, under what conditions? 5. What is the significance of the domain in defining a piecewise function? **Tip**: When dealing with piecewise functions, always check the condition on $$x$$ carefully to use the correct expression.

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Piecewise Functions
Function Evaluation
Algebra

f(x) = 2x + 3 for x < -1
f(x) = -x - 2 for x ≥ -1

Grades 9-12

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