Math Problem Statement
f(x)= ⎩ ⎨ ⎧
−(x+7) 2 +6 −4 −2x−4
for x≤−4 1 1
for −4<x≤−1 1 1
for x>−1 1 1
Find , f, of, minus, 4 Find f(−4)
Solution
Given the piecewise function:
\begin{cases} -(x + 7)^2 + 6 & \text{for } x \leq -4 \\ -4 & \text{for } -4 < x \leq -1 \\ -2x - 4 & \text{for } x > -1 \end{cases}$$ We are tasked with finding $$f(-4)$$. Since $$-4 \leq -4$$, we use the first piece of the function, which is: $$f(x) = -(x + 7)^2 + 6$$ Substitute $$x = -4$$: $$f(-4) = -((-4 + 7)^2) + 6$$ $$f(-4) = -(3^2) + 6$$ $$f(-4) = -9 + 6$$ $$f(-4) = -3$$ So, $$f(-4) = -3$$. --- Do you want more details or have any questions? Here are 5 related questions to expand on this concept: 1. What is $$f(-5)$$ for the given function? 2. How do we calculate $$f(-1)$$? 3. Can you find $$f(0)$$ for this piecewise function? 4. What does the graph of this piecewise function look like? 5. How does the first piece of the function behave as $$x \to -\infty$$? **Tip:** Always ensure that you're using the correct piece of the function by checking which interval the input falls into.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Quadratic Functions
Function Evaluation
Formulas
f(x) = -(x + 7)^2 + 6 for x ≤ -4
f(x) = -4 for -4 < x ≤ -1
f(x) = -2x - 4 for x > -1
Theorems
-
Suitable Grade Level
Grades 10-12