Math Problem Statement
Tell whether the relationship in this table represents a function.
Solution
In this table, you are asked to determine whether the relationship between the values of and represents a function.
For a relation to be a function, each input must be associated with exactly one output . In other words, no -value should have more than one corresponding -value.
Let's analyze the table:
x & 0 & 1 & 2 & 4 & 5 & 7 \\ \hline y & 6 & 4 & 1 & 0 & -2 & -5 \\ \end{array}$$ - For $$x = 0$$, $$y = 6$$ - For $$x = 1$$, $$y = 4$$ - For $$x = 2$$, $$y = 1$$ - For $$x = 4$$, $$y = 0$$ - For $$x = 5$$, $$y = -2$$ - For $$x = 7$$, $$y = -5$$ Each $$x$$-value has exactly one corresponding $$y$$-value, and no $$x$$-value repeats. Therefore, this relation *does* represent a function. You should select **"Function"**. Would you like further details or have any questions about this? Here are five questions to expand on this topic: 1. What is the formal definition of a function? 2. How can we determine if a graph represents a function? 3. What happens if an $$x$$-value is repeated in a table but has different $$y$$-values? 4. What is the difference between a function and a relation? 5. Can a function have the same $$y$$-value for multiple $$x$$-values? **Tip:** A function can pass the **vertical line test**—any vertical line drawn through its graph intersects the graph at most once.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 6-8