Functions Reference Sheet
Written by Adi Ackerman, Head Teacher
"Functions Reference Sheet" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.F.A.1. It also works a grade below or above, as a tool for a student who is ready for it or a quick refresher for an older one.
8th grade math resource: see what makes a rule a function, with input and output tables and y = 2x − 1 shown as an equation, words, a table and a graph. Part of our reference sheets functions collection. Aligned to Common Core standards.
How do I use this resource?
Hand out the Functions Reference Sheet when students start the What is a function sheets, and the linear and nonlinear guide before they classify functions. Students can keep both in a notebook for later units.
What students will practice
- Students will define a function as a rule that gives each input exactly one output.
- Students will tell a function from a relation where one input has two outputs.
- Students will connect the equation, words, table and graph of y = 2x − 1.
What Makes a Relation a Function
Functions From Sets of Ordered Pairs
Functions From Input-Output Tables
Is the Relation a Function? Mapping Diagrams
Functions From Graphs, Vertical Line Test
Check for Functions in Five Forms
Linear or Nonlinear From Graphs and Equations
Linear or Nonlinear From Tables, Constant Differences
Curriculum Links
Common Core State Standards
Functions · 8th Grade
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.
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FAQ
How do I use the Functions Reference Sheet?
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Hand out the Functions Reference Sheet when students start the What is a function sheets, and the linear and nonlinear guide before they classify functions. Students can keep both in a notebook for later units.
What is the Functions Reference Sheet?
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See what makes a rule a function, with input and output tables and y = 2x − 1 shown as an equation, words, a table and a graph.
Can I use the Functions Reference Sheet at home and in the classroom?
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Yes. We made it for 8th Grade functions, and it works the same at home or at school. At home a student can print it and keep it with their school work. Teachers print a copy per student or one for the whole room, whichever the day needs.
What makes a relation a function?
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A function gives each input exactly one output. Two inputs may share an output, but one input can never have two. The Functions Reference Sheet shows both cases in input and output tables.
How can you tell if a function is linear from a table?
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Check whether y changes by the same amount each time x goes up by 1. In the linear table on the reference sheet, y goes up 2 every time. In the nonlinear table, y goes up 1, then 3, then 5.
Can a linear function be written as y = mx + b?
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Yes. Every linear function can be written in the form y = mx + b and graphs as a straight line that is not vertical. The Linear and Nonlinear Functions Reference Sheet places this beside a curved graph for contrast.
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What Makes a Relation a Function
Functions From Sets of Ordered Pairs
Functions From Input-Output Tables
Is the Relation a Function? Mapping Diagrams
Functions From Graphs, Vertical Line Test
Check for Functions in Five Forms
Linear or Nonlinear From Graphs and Equations
Linear or Nonlinear From Tables, Constant Differences