math class 678 4-in-1 skill sheets
8.F.A.1 8th Grade Functions

Functions Definition

Understand that a function is a rule that assigns to each input exactly one output, and that the graph is the set of ordered pairs.

How to explain it

At this standard, students determine whether a relation is a function using ordered pairs, tables, mapping diagrams, and graphs, applying the vertical line test to graphical representations and identifying when any input maps to more than one output.

The anchor students hold onto: Scan inputs: if each input pairs with exactly one output, it IS a function. If any input has two different outputs (or a vertical line crosses the graph twice), it is NOT a function.

Students apply the function definition in Comparing Functions (8.F.A.2) and Graphing Linear Equations (8.F.A.3), then build and interpret linear models in 8.F.B.4 and 8.F.B.5.

Worked examples

Example 1 Function (ordered pairs)
Pairs: (1,2),(2,4),(3,6),(4,8).
Step 1Scan inputs: 1, 2, 3, 4 — each appears once.
Step 2Each input has exactly one output.
Step 3YES — this is a function.
AnswerFunction (y = 2x)
Example 2 Not a Function (mapping)
Map: 1→3, 2→5, 2→7, 3→9.
Step 1Scan inputs: 2 appears with both 5 and 7.
Step 2Input 2 maps to two different outputs.
Step 3NO — this is NOT a function.
AnswerNot a function (input 2 → two outputs)
Example 3 Function (graph / VLT)
Graph: y = 2x − 1. Function?
Step 1Draw a vertical line — it hits the graph once.
Step 2Each x-value produces exactly one y-value.
Step 3YES — linear graphs always pass the VLT.
AnswerFunction (VLT passes — line hits once)

Common mistakes

What students write Thinking a relation is not a function when two inputs share the same output (e.g., (1,4) and (2,4)).
The fix Outputs CAN repeat. The test is inputs only — each input must pair with exactly one output.
Try this Tyler examines the mapping: 1→4, 2→4, 3→8. Tyler writes: "Output 4 appears twice, so this is NOT a function." Identify Tyler's error and state the correct answer with justification.
What students write Confusing which column is the input and which is the output in a table or mapping diagram.
The fix The input (x) is always the independent variable — the left column in a table or left side of a mapping.

Teacher tip

Head off the two predictable errors before they happen. First: Outputs CAN repeat. The test is inputs only — each input must pair with exactly one output. Second: The input (x) is always the independent variable — the left column in a table or left side of a mapping.