Math Problem Statement
Calculate the following values using the given function: h(x) = 5x + 10 if x < 0, h(x) = -3x + 6 if 0 <= x < 8.
Solution
Let's go over this function and the required calculations step by step. The function is defined piecewise as:
\begin{cases} 5x + 10 & \text{if } x < 0 \\ -3x + 6 & \text{if } 0 \leq x < 8 \end{cases}$$ ### A) The value of $$h(-10)$$ Since $$-10 < 0$$, we use the first piece of the function: $$h(x) = 5x + 10$$. Substituting $$x = -10$$: $$h(-10) = 5(-10) + 10 = -50 + 10 = -40$$ So, the correct answer is that $$h(-10) = -40$$, corresponding to the first choice provided, where $$5 \cdot (-10) + 10$$ is correctly calculated. --- ### B) $$h(0)$$ For $$x = 0$$, since $$0 \leq 0 < 8$$, we use the second piece of the function: $$h(x) = -3x + 6$$. Substituting $$x = 0$$: $$h(0) = -3(0) + 6 = 0 + 6 = 6$$ Thus, $$h(0) = 6$$. --- ### C) $$h(1)$$ For $$x = 1$$, since $$0 \leq 1 < 8$$, we again use the second piece of the function: $$h(x) = -3x + 6$$. Substituting $$x = 1$$: $$h(1) = -3(1) + 6 = -3 + 6 = 3$$ So, $$h(1) = 3$$. --- ### D) The value of $$h(11)$$ The function $$h(x)$$ is only defined for $$x < 8$$. Since $$x = 11$$ is outside this domain, the function is **not defined** for $$h(11)$$. The correct answer here is the first option: "is not defined because 11 is not in the domain of $$h$$." --- Would you like further details on any of these calculations or explanations? ### Related Questions: 1. What is $$h(x)$$ for values between 0 and 8, and how does the slope of the function affect these values? 2. How can we graph the function $$h(x)$$ to better understand its behavior? 3. Why is the function $$h(x)$$ not defined for values greater than or equal to 8? 4. Can we extend the function $$h(x)$$ to be defined for values outside of $$x < 8$$? 5. What does it mean for a function to be piecewise, and how is it commonly used in real-world applications? **Tip:** Always double-check the domain of piecewise functions to ensure you’re using the correct rule for the given $$x$$-value.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Domain and Range
Linear Functions
Formulas
h(x) = 5x + 10 if x < 0
h(x) = -3x + 6 if 0 ≤ x < 8
Theorems
Piecewise Function Rules
Suitable Grade Level
Grades 9-12