Math Problem Statement
Write the piecewise function for the graph
Write the piecewise function for the graph.
Solution
The graph provided appears to depict a piecewise function , composed of three distinct linear segments. Let's analyze each section of the graph:
-
First segment (leftmost):
- This is a horizontal line on the interval with an open circle at and a closed circle at .
- The function has a constant value of over this interval.
- Equation: for .
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Second segment (middle):
- This segment is an increasing line from to , with closed circles at both endpoints.
- The slope of this line can be calculated as , and the equation of the line in point-slope form is:
- Equation: for .
-
Third segment (rightmost):
- This is another increasing line from to , with an open circle at and a closed circle at .
- The slope of this line is , and the equation of the line is:
- Equation: for .
The Piecewise Function:
\begin{cases} -9 & \text{for } -9 < x \leq -4 \\ 2x + 2 & \text{for } 1 \leq x \leq 3 \\ 2x - 10 & \text{for } 6 < x \leq 8 \end{cases}$$ Would you like a deeper explanation of any part, or do you have any specific questions? --- Here are 5 related questions: 1. How do you calculate the slope of a line between two points? 2. What is the difference between an open and a closed circle on a graph? 3. How can you derive the equation of a line given two points? 4. What is a piecewise function and how is it used in mathematics? 5. What are the conditions for a function to be continuous? **Tip:** When writing piecewise functions, always check the behavior at the endpoints (open or closed circles) to define the correct inequalities for each segment.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Equations
Graph Interpretation
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b
Theorems
Basic principles of piecewise functions
Slope-intercept form of a line
Suitable Grade Level
Grades 9-11