Math Problem Statement
Given the function f(x) as a piecewise function:
f(x) = {-x^2 - 4, x < -3; -x + 10, x >= -3}, find f(-5) and f(-1).
Solution
We are given the function as a piecewise function:
-x^2 - 4 & \text{if } x < -3 \\ -x + 10 & \text{if } x \geq -3 \end{cases}$$ We are tasked with finding $$f(-5)$$ and $$f(-1)$$. ### Step 1: Finding $$f(-5)$$ Since $$-5 < -3$$, we use the first piece of the function: $$f(x) = -x^2 - 4$$ Substituting $$x = -5$$: $$f(-5) = -(-5)^2 - 4 = -(25) - 4 = -25 - 4 = -29$$ ### Step 2: Finding $$f(-1)$$ Since $$-1 \geq -3$$, we use the second piece of the function: $$f(x) = -x + 10$$ Substituting $$x = -1$$: $$f(-1) = -(-1) + 10 = 1 + 10 = 11$$ ### Final Answers: $$f(-5) = -29$$ $$f(-1) = 11$$ Do you need further clarification or have any other questions? Here are 5 related questions to explore further: 1. What would $$f(0)$$ be, given the same piecewise function? 2. How do we determine which piece of a piecewise function to use for a given value of $$x$$? 3. What is the domain of this piecewise function? 4. How would the graph of this function look? 5. Can you solve for $$f(-3)$$, and which piece would you use? **Tip**: Always verify which part of a piecewise function applies by checking the conditions on $$x$$ before substituting the value into the function.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Quadratic Functions
Linear Functions
Formulas
f(x) = -x^2 - 4 for x < -3
f(x) = -x + 10 for x >= -3
Theorems
-
Suitable Grade Level
Grades 9-12