Functions
Lessons in this chapter
About Functions
Functions introduces function as a formal concept for the first time, then connects it immediately to the linear equations already familiar from this grade.
Relations, Functions and their Representations distinguishes a function from a general relation: a function pairs every input with exactly one output, and shows the same function represented as a table, a graph, an equation, and a mapping diagram.
Linear Functions applies that new vocabulary to the linear equations already covered in Graphing and Writing Linear Equations, framing y = mx + b as a rule that takes an input x and produces exactly one output y.
Both lessons, Relations, Functions and their Representations and Linear Functions, are 8th grade math worksheets worked in the page rather than explanations to read. The questions ask your child to test tables, graphs and mapping diagrams against the one output per input rule, and each answer is marked as it goes in. Both are free to try, with no login needed for your first 3.
Frequently asked questions
Relations, Functions and their Representations introduces the rule that a function pairs each input with exactly one output, and has your child apply it across tables, graphs, equations and mapping diagrams, including the vertical line test. Linear Functions then narrows to functions of the form y = mx + b, whose graphs are straight lines, connecting the idea back to the slope-intercept work from Graphing and Writing Linear Equations. This sits in the Common Core domain Functions (8.F).
A function is a rule that pairs every input with exactly one output: for any input value, a function gives back one, and only one, corresponding output.
A relation is just any pairing between inputs and outputs, but a function has the added rule that no input can be paired with more than one output: Relations, Functions and their Representations has kids check this "one output per input" rule across tables, graphs, and mapping diagrams.
The same function can be shown as a table of input-output pairs, a graph of points, an equation, or a mapping diagram connecting inputs to outputs: all four represent the identical rule, just in different formats.
A linear function's rule can be written as y = mx + b, and its graph is always a straight line: Linear Functions connects this directly to the slope-intercept work from Graphing and Writing Linear Equations.
Use the vertical line test: if any vertical line drawn on the graph crosses the curve more than once, the relation is not a function, since that would mean one input has more than one output.