8.F.1: What a Function Is
Also written as 8.F.A.1 and CCSS.MATH.CONTENT.8.F.A.1 · Cluster: Define, evaluate, and compare functions.
The Official Wording
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Common Core State Standards, Grade 8, Functions · Read it at the source · Checked October 14, 2026
What 8.F.1 Means in Plain English
Eighth graders ask one question of every rule, table or graph: does each input get exactly one output? The pairs (1, 3), (2, 5), (3, 7) make a function. A table that sends 2 to both 5 and 9 does not, and students say why.
They also see that a graph is just every input-output pair plotted as a point, so a vertical line can never cross it twice. Function notation like f(x) waits for high school (HSF-IF.1), where the same idea gets the words domain and range.
8.F.1 I Can Statements
- I can tell whether a table or set of pairs is a function.
- I can explain why one input with two outputs breaks the rule.
- I can plot a function’s input-output pairs as points on a graph.
8.F.1 Worked Example
Two tables from the same worksheet, and only one of them is a function.
Table A: inputs 1, 2, 3, 4 give outputs 5, 8, 11, 14. Table B: inputs 1, 2, 2, 3 give outputs 4, 6, 7, 9. Which table shows a function?
- A function has to give exactly one output for each input, so check the input column first, not the outputs.Check: does any input repeat with a different output?
- Table A: the inputs 1, 2, 3, 4 are all different, so each one has only one output. The outputs happen to go up by 3 each time, but that is not what makes it a function.Table A: (1, 5), (2, 8), (3, 11), (4, 14), a function
- Table B: the input 2 appears twice, once with output 6 and once with output 7. One input, two outputs.Table B: (2, 6) and (2, 7), not a function
- Plot Table A. The four points are its graph: the set of its input-output pairs. Plotting Table B puts two points on the vertical line x = 2.Graph of A: the points (1, 5), (2, 8), (3, 11), (4, 14)
Check it: Run a pencil straight up and down each graph. On Table A’s points it never touches two at once; on Table B’s it touches (2, 6) and (2, 7) together.
Common Mistakes with 8.F.1
Rejecting repeated outputs
“(1, 4), (2, 4), (3, 4) is not a function because 4 repeats.”
Try this: Point to the input column only. Different inputs may share an output, and y = 4 for every x is still a function.
Reading the pairs backwards
(2, 6) and (3, 6) called “two outputs for the input 6”
Try this: Label the columns input and output before anything else, and read every pair as (input, output), the x value first.
Thinking a function must have a pattern
“(1, 7), (2, 3), (3, 12) is not a function because there is no rule.”
Try this: Separate the two ideas: a function only needs one output per input. A pattern is a bonus, not a requirement.
Where 8.F.1 Fits
Practice 8.F.1
Quick Check
- Is the set of pairs (0, 2), (1, 5), (2, 8), (3, 11) a function?
- Is the set of pairs (4, 1), (5, 1), (4, 3) a function?
- A rule triples the input and adds 1. What are the ordered pairs for inputs 0, 1, 2, and what would the graph show?