Pre-Algebra
Functions (introductory)
Definition of a function
20 practice questions
0 video lessons
Theory + worked examples
Definition of a Function
Texas Pre-Algebra (TEKS) • Standard 8.5(G) • Functions
Definition of a Function is the opening topic of Functions in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.5(G), which requires students to understand and identify functions as one output per input.
A function assigns exactly one output to each input; the vertical line test checks this on a graph.
Theory
A function is a rule that assigns exactly one output to each input.
Vertical line test: a graph is a function if no vertical line meets it more than once.
Each input maps to one output.
What makes a function.
The rule:
\[\text{each input}\to\text{exactly one output}\]
An input can repeat an output, but not have two.
How to test for a function
- List the input-output pairs.
- Check no input has two outputs.
- On a graph, use the vertical line test.
- If it passes, it is a function.
Example 1 — Is it a function?
Does \(\{(1,2),(2,4),(3,6)\}\) define a function?
Solution
Each input has one output — yes.
Example 2 — Not a function
Is \(\{(1,2),(1,3)\}\) a function?
Solution
Input \(1\) has two outputs — no.
Example 3 — Vertical line test
How does a graph fail to be a function?
Solution
If a vertical line crosses it more than once.
Example 4 — Evaluate
For the mapping above, what is the output for input \(2\)?
Solution
Read the pair \((2,4)\).
| \(4\) |
Common pitfalls
One input, two outputs is not a function.
Two inputs sharing an output is fine.
Use vertical lines, not horizontal, for the test.
Frequently asked questions
What is a function?
A rule assigning one output to each input.
What is the vertical line test?
A graph is a function if no vertical line hits it twice.
Can two inputs share an output?
Yes.
Is \(\{(1,2),(1,3)\}\) a function?
No.
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