Math Problem Statement
Graph the piecewise function f(x) where f(x) = -1/3x + 3 for -6 <= x <= -3 and f(x) = 4 for -3 < x < 5.
Solution
Here's the graph of the given piecewise function :
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The blue line represents the linear segment for .
- The filled blue circle at indicates the endpoint where the first piece ends.
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The green horizontal line represents the constant value for .
- The open green circle at indicates a discontinuity, showing that is not defined as 4 at , but immediately jumps from 3 to 4 after this point.
Would you like more details on the graph or any clarifications?
Here are some related questions for further exploration:
- How do you find the slope of a line from its equation?
- How does the graph of a constant function look like, and why?
- What happens when there is a discontinuity in a piecewise function?
- How would you graph a quadratic function as part of a piecewise function?
- What are the conditions for a function to be continuous at a given point?
Tip: Always look at endpoints carefully when graphing piecewise functions. Some are included (closed circle), while others are not (open circle).
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Graphing Linear Functions
Constant Functions
Discontinuities
Formulas
f(x) = -1/3x + 3
f(x) = 4
Theorems
Graphing Piecewise Functions
Continuity and Discontinuity Theorems
Suitable Grade Level
Grades 9-12