Math Problem Statement
Determine whether each relation is a function.
x: 3, 4, 3, 5
y: 7, 2, 2, 1
Solution
To determine whether the given relation is a function, we need to check if every input is associated with exactly one output . A relation is not a function if any -value is paired with more than one -value.
From the table:
\hline x & y \\ \hline 3 & 7 \\ 4 & 2 \\ 3 & 2 \\ 5 & 1 \\ \hline \end{array}$$ ### Analysis: - The $$x$$-value 3 is paired with two different $$y$$-values (7 and 2). - This means the same $$x$$-value (3) is associated with multiple $$y$$-values. ### Conclusion: This relation is **not a function**, because for the input $$x = 3$$, there are two different outputs. Would you like further explanation or have any questions? Here are five related questions you might consider: 1. What is the definition of a function in mathematics? 2. How can you graphically determine if a relation is a function? 3. Can a function have the same $$y$$-value for different $$x$$-values? 4. What are some examples of real-life functions? 5. How does the vertical line test help in identifying functions? **Tip:** A quick way to check if a relation is a function is to ensure no $$x$$-value repeats with different $$y$$-values.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Functions
Relations
Input-Output Mapping
Formulas
-
Theorems
Definition of a Function
Suitable Grade Level
Grades 8-10