AlgebraStructure & Method · Book 1All Chapters

Functions

8-6Functions Defined by Tables and Graphs

Overview

A function pairs each input with exactly one output. Tables and graphs can show functions visually.

Key ideas

  • No x-value repeats with a different y.
  • Vertical Line Test: a graph is a function if no vertical line hits it more than once.
  • Domain = inputs; range = outputs.

Worked examples

Example 1

Problem. Is {(1,2), (2,4), (3,6)} a function?

Solution. Yes — each x has one y.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Is {(1,2), (1,3)} a function?

  2. 2.

    Domain of {(0,1),(2,3),(4,5)}?

  3. 3.

    Does a circle pass the vertical line test?

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    From a table, x: 1,2,3,4 and y: 3,5,7,9. Is this a function? What is the rule?

  2. 2.

    A graph passes the vertical line test. Is it a function? Explain.