Functions and graphs

Ages 13 to 17 Read alone · about 40 minutes

Read together

A function is a rule that gives exactly one output for each input. We can show it as a table, a formula or a graph.

For y = 2x + 1, x = 3 gives y = 7.

Do it

1. Make a table for y = 2x + 1 with x from 0 to 5.
2. Plot the points on a grid and join them. What shape is it?
3. Change the 2 and the 1 and see how the line tilts and moves.
4. Find a real situation that fits: for example, a fixed fee plus a price per hour.

Talk about it

• What does the slope tell us?
• What does the y-intercept mean in the real situation?

For the grown-up

Functions are the foundation of algebra and calculus. Connecting a formula, a table and a graph is the key habit.

Mark as done

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Where this comes from

• National Governors Association Center for Best Practices and Council of Chief State School Officers, Common Core State Standards for Mathematics (2010), standard 8.F.A (define, evaluate and compare functions)
• National Council of Teachers of Mathematics, Principles to Actions: Ensuring Mathematical Success for All (2014)

Written with AI assistance and checked against the sources listed. Please read it before sharing it with a child.