Math Problem Statement
State the domain and range of the relation given in the table below, and determine if it is a function.
Solution
Let's first examine the table to extract the information needed to find the domain, range, and whether the relation is a function.
The relation is given as pairs of values:
x & -2 & 17 & -1 & -1 & 12 & 16 \\ y & -11 & 3 & 0 & -7 & 11 & 21 \\ \end{array}$$ ### 1. **Domain**: The domain is the set of all possible $$x$$-values. From the table, the $$x$$-values are: $$\{-2, 17, -1, 12, 16\}$$ Since the value $$-1$$ appears twice, we only list it once. The domain is: $$\{-2, 17, -1, 12, 16\}$$ ### 2. **Range**: The range is the set of all possible $$y$$-values. From the table, the $$y$$-values are: $$\{-11, 3, 0, -7, 11, 21\}$$ The range is: $$\{-11, 3, 0, -7, 11, 21\}$$ ### 3. **Is it a function?**: A relation is a function if each $$x$$-value corresponds to exactly one $$y$$-value. In the table, we see that the $$x$$-value $$-1$$ is paired with two different $$y$$-values: 0 and -7. This means the same $$x$$-value is associated with more than one $$y$$-value, so the relation **is not a function**. ### Summary: - **Domain**: $$\{-2, 17, -1, 12, 16\}$$ - **Range**: $$\{-11, 3, 0, -7, 11, 21\}$$ - **Function**: No, the relation is not a function because $$x = -1$$ is associated with two different $$y$$-values. Would you like more details or have any questions about this? Here are 5 follow-up questions you might consider: 1. What makes a relation a function mathematically? 2. How can you identify the domain and range in a graph instead of a table? 3. How can you express this relation as a set of ordered pairs? 4. What are the properties of a one-to-one function? 5. How could this relation be modified to become a function? **Tip**: To check if a relation is a function, make sure no $$x$$-value is repeated with different $$y$$-values. This is called the "vertical line test" for functions.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Domain and Range
Formulas
-
Theorems
Definition of a Function
Vertical Line Test
Suitable Grade Level
Grades 9-11
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