Math Problem Statement
answer
Express the function graphed on the axes below as a piecewise function.
Solution
To express the function shown in the graph as a piecewise function, we need to analyze the behavior of the function on different intervals of the x-axis.
From the graph:
- For , the function is a horizontal line at . This section includes a solid point at , which means the function is defined as for .
- For , there is no defined value at , as the function has an open circle at .
- For , the function is a horizontal line at , but the function is not defined at because of the open circle.
Piecewise function:
\begin{cases} -4 & \text{for } x \leq -1 \\ 5 & \text{for } x > 0 \end{cases}$$ This represents the behavior of the function in different parts of the graph. Would you like further clarification or details on how the function was derived? Here are 5 related questions for further exploration: 1. How would the piecewise function change if there were a defined value at $$x = 0$$? 2. What is the significance of the open and closed circles in defining piecewise functions? 3. Can a piecewise function have more than two intervals? What would that look like graphically? 4. How would you calculate the domain and range of this piecewise function? 5. What are common applications of piecewise functions in real-life problems? **Tip:** Always check for open and closed circles in a graph, as they determine whether the function is defined or undefined at certain points.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Function Behavior Analysis
Graph Interpretation
Formulas
Piecewise Function Definition
Theorems
Properties of Piecewise Functions
Suitable Grade Level
Grades 9-11