CCSS.Math.Content.8.F.A.1
The Standard
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 for Mathematics · Functions
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether tables, mappings, ordered pairs, and graphs represent functions. They explain why one input cannot be matched with two different outputs and read graphed points as ordered pairs.
What Mastery Looks Like
- Given a table, mapping, graph, or set of ordered pairs, students correctly decide whether it represents a function. They identify any input paired with different outputs and explain their decision.
Common Misconceptions
- Students may think repeated outputs mean a relation is not a function. They may also miss repeated inputs with different outputs or reverse the coordinates in an ordered pair.
How to Assess It
- Exit ticket: Which relation is a function, A: {(1,4), (2,4), (3,5)} or B: {(1,4), (1,5), (3,5)}? Explain using the inputs.
Lesson moves
Ways to Teach It
Give groups coordinate cards and two hoops labeled function and not a function, then have them sort and defend each placement.
Use student name as input and locker number as output; ask which repeats are allowed, then have students justify their answer.
Play Function Detective: reveal tables, mappings, and graphs one at a time; teams hold up function or not function cards and explain.
Examine a vending machine menu, treating each code as an input, and decide whether two products for one code would represent a function.
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Printable 8.F.A.1 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.8.F.A.1, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.EE.C.9
Using variables, tables, graphs, and dependent versus independent quantities prepares students to see functions as input-output rules.
- CCSS.Math.Content.6.NS.C.6c
Plotting ordered pairs on the coordinate plane supports seeing a function graph as input-output pairs.
- CCSS.Math.Content.6.EE.A.2
Evaluating expressions with letters supports finding outputs from input rules and connecting those values to ordered pairs.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSA-REI.D.10
Function graphs introduce graphs as ordered pairs, supporting the shift to equations whose graphs include all solution pairs.
- CCSS.Math.Content.8.F.A.3
Students must understand inputs, outputs, and function graphs before interpreting y = mx + b as a linear function.
- CCSS.Math.Content.8.F.A.2
Students must understand inputs, outputs, and graphs as function pairs before comparing function properties across equations, tables, graphs, or descriptions.
- CCSS.Math.Content.8.F.B.5
Knowing a function pairs each input with one output supports interpreting graphs as relationships to describe and sketch their features.
- CCSS.Math.Content.HSF-IF.B.4
Interpreting function graphs and tables relies on seeing each point as an input-output pair tied to the quantities.
- CCSS.Math.Content.HSF-IF.C.9
Comparing functions across tables, graphs, formulas, and words requires understanding inputs, outputs, and graph points as paired values.
Keep exploring
Related Standards
- CCSS.Math.Content.HSF-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the r...
- CCSS.Math.Content.HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pa...
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