Math Problem Statement
For the piecewise function, find the values h(-5), h(0), h(5), and h(9):
h(x) =
-2x - 16 for x < -4
5 for -4 ≤ x < 5
x + 7 for x ≥ 5
Solution
We are given a piecewise function defined as follows:
\begin{cases} -2x - 16 & \text{for } x < -4 \\ 5 & \text{for } -4 \leq x < 5 \\ x + 7 & \text{for } x \geq 5 \end{cases}$$ We need to evaluate the function at the given points: $$h(-5)$$, $$h(0)$$, $$h(5)$$, and $$h(9)$$. ### Step-by-step evaluation: 1. **For $$h(-5)$$:** Since $$-5 < -4$$, we use the first part of the piecewise function: $$h(x) = -2x - 16$$. $$h(-5) = -2(-5) - 16 = 10 - 16 = -6$$ 2. **For $$h(0)$$:** Since $$-4 \leq 0 < 5$$, we use the second part of the piecewise function: $$h(x) = 5$$. $$h(0) = 5$$ 3. **For $$h(5)$$:** Since $$5 \geq 5$$, we use the third part of the piecewise function: $$h(x) = x + 7$$. $$h(5) = 5 + 7 = 12$$ 4. **For $$h(9)$$:** Since $$9 \geq 5$$, we use the third part of the piecewise function: $$h(x) = x + 7$$. $$h(9) = 9 + 7 = 16$$ ### Final answers: - $$h(-5) = -6$$ - $$h(0) = 5$$ - $$h(5) = 12$$ - $$h(9) = 16$$ Let me know if you need more details or have any questions! Here are 5 related questions for further practice: 1. What is $$h(-4)$$? 2. What is the domain of the function $$h(x)$$? 3. Determine if the function is continuous at $$x = -4$$. 4. Evaluate $$h(-10)$$. 5. Solve for $$x$$ if $$h(x) = 0$$. **Tip:** When working with piecewise functions, always carefully check which piece applies to the given input value based on the conditions provided.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Evaluation
Algebra
Formulas
h(x) = -2x - 16 for x < -4
h(x) = 5 for -4 ≤ x < 5
h(x) = x + 7 for x ≥ 5
Theorems
-
Suitable Grade Level
Grades 9-11