Math Problem Statement
Graph the function h(x), a piecewise function with intervals and corresponding values provided.
Solution
The function is a piecewise function defined as follows:
-1 & \text{if } -2.5 \leq x \leq -1.5 \\ 0 & \text{if } -1.5 < x \leq -0.5 \\ 1 & \text{if } -0.5 < x \leq 0.5 \\ 2 & \text{if } 0.5 < x \leq 1.5 \\ 3 & \text{if } 1.5 < x \leq 2.5 \end{cases}$$ We can graph this piecewise function by plotting the values of $$h(x)$$ for the corresponding intervals of $$x$$. 1. For $$-2.5 \leq x \leq -1.5$$, $$h(x) = -1$$ (a horizontal line at $$y = -1$$). 2. For $$-1.5 < x \leq -0.5$$, $$h(x) = 0$$ (a horizontal line at $$y = 0$$). 3. For $$-0.5 < x \leq 0.5$$, $$h(x) = 1$$ (a horizontal line at $$y = 1$$). 4. For $$0.5 < x \leq 1.5$$, $$h(x) = 2$$ (a horizontal line at $$y = 2$$). 5. For $$1.5 < x \leq 2.5$$, $$h(x) = 3$$ (a horizontal line at $$y = 3$$). The function jumps at the boundaries of each interval, but it's continuous within the intervals. The graph will have open circles where the intervals break (except at the endpoints where the inequality includes the boundary). Would you like me to create a graph of this function for you? Let me know if you'd like more details on any part, and here are some related questions you could explore: 1. How do you handle open and closed circles when graphing piecewise functions? 2. What is the difference between continuous and discontinuous piecewise functions? 3. How does the value of the function change between intervals? 4. How can you determine if a piecewise function is defined for all real numbers? 5. How would the graph change if you altered the range of one of the intervals? **Tip:** When graphing piecewise functions, always check whether to include or exclude the endpoints for each interval based on the inequalities.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Graphing Functions
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12