Example Card：Determining If a Set of Ordered Pairs Is a Function
Determine if ordered pairs form a function in Grade 9 algebra by verifying each x-value maps to exactly one y-value, using mapping diagrams or the vertical-line test for graphs.
Key Concepts
Let's investigate if every input in this relation gets exactly one output—this is the crux of telling a function apart from just a general relation.
Example Problem: Determine whether $\{(6, 5), (9, 4), (2, 2), (8, 7), (6, 1)\}$ represents a function.
Step by Step: 1. Examine the domain values: $6, 9, 2, 8, 6$. Notice that $6$ appears twice. 2. Check which range values the repeated domain value ($6$) maps to: $6 \rightarrow 5$ and $6 \rightarrow 1$. 3. Since $6$ maps to two different range values, the rule for functions is broken (each input should go to exactly one output).
Common Questions
How do you determine if a set of ordered pairs is a function?
Check whether each x-value (input) appears only once in the set. If any x-value is paired with two or more different y-values, the relation is NOT a function. Every input must have exactly one output.
What is a mapping diagram and how does it identify functions?
A mapping diagram draws arrows from each x-value to its corresponding y-value. If every x-value has exactly one arrow pointing to a y-value, the relation is a function. Multiple arrows from a single x indicate it is not a function.
Can the same y-value appear multiple times in a function?
Yes. Multiple x-values can map to the same y-value and still be a function. For instance, {(1,3), (2,3), (5,3)} is a function because each x (1, 2, 5) has only one y-output (3).