Math Problem Statement
make a piecewise for h(x) and g(x)
Solution
To create piecewise functions for and , we need to define different expressions for these functions, based on intervals of . Here's a general example of how you can construct piecewise functions:
Example for :
\begin{cases} x^2 + 1 & \text{if } x \leq 0 \\ 2x - 3 & \text{if } 0 < x < 3 \\ 4x + 2 & \text{if } x \geq 3 \end{cases}$$ ### Example for $$g(x)$$: $$g(x) = \begin{cases} \sin(x) & \text{if } x < \pi \\ x^3 & \text{if } x = \pi \\ \ln(x) & \text{if } x > \pi \end{cases}$$ This is just an illustrative example. You can define the specific intervals and expressions for $$h(x)$$ and $$g(x)$$ as needed. --- Would you like to provide different conditions or expressions for $$h(x)$$ and $$g(x)$$? Here are five questions to expand your understanding: 1. What specific conditions or intervals should $$h(x)$$ and $$g(x)$$ follow? 2. Do you need to ensure continuity between the segments of the piecewise functions? 3. Should $$h(x)$$ or $$g(x)$$ model any specific real-world situation? 4. Would you like me to include any boundary values for $$x$$? 5. Are you looking to graph these piecewise functions? **Tip:** When constructing piecewise functions, always ensure that the intervals you choose fully cover the domain of the function without overlap unless intentional.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Intervals
Trigonometry
Logarithms
Formulas
h(x) = \begin{cases} x^2 + 1 & \text{if } x \leq 0 \\ 2x - 3 & \text{if } 0 < x < 3 \\ 4x + 2 & \text{if } x \geq 3 \end{cases}
g(x) = \begin{cases} \sin(x) & \text{if } x < \pi \\ x^3 & \text{if } x = \pi \\ \ln(x) & \text{if } x > \pi \end{cases}
Theorems
Basic Properties of Piecewise Functions
Continuity of Functions
Suitable Grade Level
Grades 9-12