Math Problem Statement

Suppose that the function h is defined as follows: h(x) = -3 if -2.5 <= x < -1.5 -2 if -1.5 <= x < -0.5 -1 if -0.5 <= x < 0.5 0 if 0.5 <= x < 1.5 1 if 1.5 <= x < 2.5 Graph the function h.

Solution

The function h(x)h(x) is defined as a piecewise function, and we need to graph it based on the following conditions:

\begin{cases} -3 & \text{if } -2.5 \leq x < -1.5 \\ -2 & \text{if } -1.5 \leq x < -0.5 \\ -1 & \text{if } -0.5 \leq x < 0.5 \\ 0 & \text{if } 0.5 \leq x < 1.5 \\ 1 & \text{if } 1.5 \leq x < 2.5 \end{cases}$$ To graph this function, you'll plot the value of $$h(x)$$ for each given interval. For example: - From $$-2.5$$ to $$-1.5$$, $$h(x) = -3$$, so you plot a horizontal line at $$y = -3$$ for this interval. - Similarly, plot horizontal lines for each of the other intervals, changing the value of $$h(x)$$ according to the given function. Would you like a detailed step-by-step explanation of how to graph this piecewise function, or are you looking for something else?

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Graphing Functions
Intervals

Formulas

Piecewise Function Definition

Theorems

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Suitable Grade Level

Grades 9-11