Math Problem Statement
Find h(5) using the given piecewise function.
Solution
The image shows a piecewise function , defined as follows:
\begin{cases} -x^2, & \text{if } x \leq -2 \\ 3, & \text{if } -2 \leq x < 0 \\ x + 2, & \text{if } x \geq 0 \end{cases}$$ We are asked to find $$h(5)$$, which appears to mean $$f(5)$$, since no separate function $$h(x)$$ is provided. So we will evaluate $$f(5)$$ using the appropriate part of the piecewise function. Since $$5 \geq 0$$, we use the third part of the function: $$f(x) = x + 2$$. Now, substitute $$x = 5$$ into this equation: $$f(5) = 5 + 2 = 7$$ Thus, $$f(5) = 7$$. Would you like more details or have any questions? --- Here are 5 related questions for further exploration: 1. What would $$f(-3)$$ be for this function? 2. How does the piecewise function change for values of $$x$$ between $$-2$$ and $$0$$? 3. Can you graph this piecewise function for a better understanding? 4. How do you handle discontinuities in piecewise functions like this one? 5. What is the domain and range of this function? **Tip**: When evaluating piecewise functions, always check which condition applies to your specific $$x$$-value before substituting.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Formulas
Piecewise function evaluation
Theorems
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Suitable Grade Level
Grades 9-11