Piecewise Function Evaluation - Find h(-7), h(-6), h(1), and h(2)

Math Problem Statement

For the piecewise function h(x) = {-4x - 20 for x < -7, 1 for -7 <= x < 1, x + 7 for x >= 1}, find the values of h(-7), h(-6), h(1), and h(2).

The problem asks you to find the values of $h(-7)$ , $h(-6)$ , $h(1)$ , and $h(2)$ for the piecewise function defined as:

\begin{cases} -4x - 20 & \text{for } x < -7 \\ 1 & \text{for } -7 \leq x < 1 \\ x + 7 & \text{for } x \geq 1 \end{cases}$$ Let’s evaluate each one step by step: 1. **For $$h(-7)$$:** - Since $$-7 \leq x < 1$$, the second condition applies. - So, $$h(-7) = 1$$. 2. **For $$h(-6)$$:** - Since $$-7 \leq x < 1$$, the second condition applies. - So, $$h(-6) = 1$$. 3. **For $$h(1)$$:** - Since $$x \geq 1$$, the third condition applies. - So, $$h(1) = 1 + 7 = 8$$. 4. **For $$h(2)$$:** - Since $$x \geq 1$$, the third condition applies. - So, $$h(2) = 2 + 7 = 9$$. ### Final Answers: - $$h(-7) = 1$$ - $$h(-6) = 1$$ - $$h(1) = 8$$ - $$h(2) = 9$$ Would you like further clarification on any of these steps? Here are 5 related questions to help deepen your understanding: 1. How would the function change if the condition for $$h(x)$$ was $$-5 \leq x < 1$$ instead of $$-7 \leq x < 1$$? 2. What is the significance of having different expressions for different ranges of $$x$$ in piecewise functions? 3. Can you graph the given piecewise function and identify any discontinuities? 4. How would you compute $$h(x)$$ for a value of $$x = -8$$? 5. What happens to the function as $$x$$ approaches 1 from both sides? **Tip:** In piecewise functions, always start by identifying which condition the input value falls under before solving.

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Piecewise Functions
Function Evaluation

For x < -7: h(x) = -4x - 20
For -7 <= x < 1: h(x) = 1
For x >= 1: h(x) = x + 7

Grades 9-12

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