Linear and Nonlinear Functions Reference Sheet
Written by Adi Ackerman, Head Teacher
"Linear and Nonlinear Functions Reference Sheet" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.F.A.3. 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: tell linear from nonlinear functions by graph, table and equation, with tables that rise by 2 or by 1, 3, 5. 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 recognize a linear function as a graph that is a straight, nonvertical line.
- Students will check a table for a constant rate of change, such as y rising by 2 each time.
- Students will decide whether an equation can be written in the form y = mx + b.
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: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
View all 8.F.A.3 worksheets →Find this in the curriculum
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FAQ
How do I use the Linear and Nonlinear 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 Linear and Nonlinear Functions Reference Sheet?
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Tell linear from nonlinear functions by graph, table and equation, with tables that rise by 2 or by 1, 3, 5.
Can I use the Linear and Nonlinear 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