BackCollege Algebra Study Guidance – Functions, Graphs, and Transformations
Study Guide - Smart Notes
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Q4. Does the table of x and y-values represent a function? Also, find the domain and range.
Background
Topic: Functions and Relations
This question tests your understanding of what makes a relation a function, and how to identify the domain and range from a table of values.
Key Terms:
Function: A relation in which each input (x-value) corresponds to exactly one output (y-value).
Domain: The set of all possible input values (x-values).
Range: The set of all possible output values (y-values).
Step-by-Step Guidance
Examine the table to see if any x-value is repeated with a different y-value. If each x-value is paired with only one y-value, the relation is a function.
List all the x-values in the table to determine the domain. The domain is the set of all unique x-values.
List all the y-values in the table to determine the range. The range is the set of all unique y-values.
Check your lists to ensure you have not missed any values and that each value is only listed once.
Try solving on your own before revealing the answer!
Final Answer:
The table does represent a function because each x-value is paired with only one y-value.
Domain: {-5, -9, -17}; Range: {5, 9, 17}
Each x-value is unique, and each y-value is unique, so the domain and range are the sets listed above.
