Math Problem Statement
give specific answer according to the answer options
Which table of values represents a function?
Solution
To determine whether each table represents a function, we need to check if every input has only one corresponding output . In a function, no -value can be paired with more than one -value.
Left Table:
The table is:
\hline x & y \\ \hline -5 & 10 \\ -3 & 5 \\ -3 & 4 \\ 0 & 0 \\ 5 & -10 \\ \hline \end{array}$$ Here, the $$x$$-value $$-3$$ corresponds to two different $$y$$-values: $$5$$ and $$4$$. This violates the definition of a function, so **this table does not represent a function**. ### Right Table: The table is: $$\begin{array}{|c|c|} \hline x & y \\ \hline -2 & -3 \\ -1 & -2 \\ 0 & -1 \\ 0 & 0 \\ 1 & -1 \\ \hline \end{array}$$ Here, the $$x$$-value $$0$$ corresponds to two different $$y$$-values: $$-1$$ and $$0$$. This also violates the definition of a function, so **this table does not represent a function either**. ### Final Conclusion: Neither of the tables represents a function, based on the given definitions. --- Would you like more details or have any further questions? Here are some related questions you might find useful: 1. What are the key properties of a function? 2. How can I tell if a graph represents a function? 3. What is the vertical line test, and how does it relate to functions? 4. Can a function have repeating $$y$$-values? 5. What is the difference between a function and a relation? **Tip:** A quick way to check if a set of values is a function is to see if any $$x$$-value is paired with more than one $$y$$-value. If it is, the set does not represent a function.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Formulas
-
Theorems
Definition of a function
Suitable Grade Level
Grades 7-10