Free Printable Function Notation Worksheets for Year 8

In 8th grade, students formally learn the definition of a function: a rule that assigns to each input exactly one output. They use function notation to represent linear functions, compare their properties in different forms (equation, table, graph), and interpret f(x) as the y-value on the graph of f.

Introduce the concept using the vertical line test on graphs. Show examples of relations that are functions and relations that are not. Emphasize the "one unique output for every input" rule, and use mapping diagrams to visually represent this concept before moving to f(x) notation.

Eighth graders should practice identifying functions from graphs, tables, and sets of ordered pairs. They should also be comfortable evaluating linear functions written in f(x) notation and graphing them on the coordinate plane. Comparing two functions represented in different ways is also a key skill.

A common mistake is confusing the graph of x = 3 (a vertical line, not a function) with y = 3 or f(x) = 3 (a horizontal line, which is a function). Students also frequently mix up the independent (x) and dependent (f(x)) variables when interpreting real-world problems.

This topic is central to the Grade 8 Common Core standards for Functions. Specifically, standard 8.F.A.1 requires students to understand that a function is a rule assigning a unique output to each input. These worksheets provide practice for this and for 8.F.A.2, which involves comparing functions represented in different ways.

This worksheet is available as both a printable PDF and an interactive digital quiz on Wayground. The printable version is great for in-class work or homework and comes with a full answer key. The digital format allows for automatic grading and provides immediate feedback to students.