Math Problem Statement
Suppose that the function h(x) is defined as follows:
h(x) = 2 if x ≠ 0
h(x) = -4 if x = 0
Graph the function h.
Solution
The problem in the image describes a piecewise function defined as:
\begin{cases} 2 & \text{if } x \neq 0 \\ -4 & \text{if } x = 0 \end{cases}$$ ### To graph this function: 1. **Plot the point** at $$(0, -4)$$, since when $$x = 0$$, the function value is $$-4$$. This point should be represented as a closed dot to indicate that it is included in the graph. 2. **Draw a horizontal line** at $$y = 2$$ for all other $$x$$-values ($$x \neq 0$$). However, make sure there is an open circle at $$(0, 2)$$ to show that the value of the function is not 2 when $$x = 0$$. ### Steps for the graph: - **Closed dot** at $$(0, -4)$$. - **Horizontal line** at $$y = 2$$, extending to both sides of the $$y$$-axis, with an **open circle** at $$(0, 2)$$. Would you like a more detailed explanation or have any questions about this? Here are some related questions to expand your understanding: 1. What does it mean for a function to be piecewise-defined? 2. How do you determine the domain and range of a piecewise function? 3. What are the conditions for continuity in a piecewise function? 4. How does one handle open and closed circles when graphing piecewise functions? 5. How can piecewise functions be used to model real-world situations? **Tip:** Always use open and closed circles to clearly distinguish where the function values are included or excluded.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Graphing
Functions
Formulas
Piecewise function
Theorems
Graphing of Piecewise Functions
Open and Closed Circles in Graphing
Suitable Grade Level
Grades 9-11