Math Problem Statement
Tell whether the relationship in this table represents a function.
Solution
To determine whether the relationship in the table represents a function, we need to check if each input (value of ) corresponds to exactly one output (value of ).
The table provided is:
\hline x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline y & 4 & 2 & 1 & 2 & -5 & -7 \\ \hline \end{array}$$ A relationship is considered a function if each $$x$$ value has only one unique $$y$$ value. Let's verify: - For $$x = -2$$, $$y = 4$$ - For $$x = -1$$, $$y = 2$$ - For $$x = 0$$, $$y = 1$$ - For $$x = 1$$, $$y = 2$$ - For $$x = 2$$, $$y = -5$$ - For $$x = 3$$, $$y = -7$$ Each $$x$$ value has exactly one corresponding $$y$$ value, and no $$x$$ value is repeated. Therefore, **the relationship represents a function**. Would you like further clarification or details? Here are some follow-up questions you might find helpful: 1. What makes a relation not a function? 2. How can we represent this function graphically? 3. What happens if two different $$y$$ values correspond to the same $$x$$ value? 4. Can a function have repeating $$y$$ values for different $$x$$ values? 5. What is the vertical line test, and how does it relate to functions? **Tip:** A relation is not a function if one $$x$$-value corresponds to multiple $$y$$-values!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Formulas
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Theorems
Function definition: Each input corresponds to exactly one output.
Suitable Grade Level
Grades 7-9