Functions

Use function notation to make meaningful connections between expressions, tables, and other mathematical objects. Autofill tables by defining column headers with functions, or build a movable point to trace a path along a particular curve. Get started with the video on the right, then dive deeper with the resources and challenges below.

Pro-Tips

You can evaluate a function at a certain point:

f\left(x\right)=x^{2}+3x. Evaluated at f\left(3\right) is 18. Screenshot.

You can use the notation f(x,y), for example, to define a function with more than one variable:

f\left(x,y\right)=x^{2}+3y. Evaluated at f\left(10,3\right) is 109. Screenshot.

Defining a function once allows you to use this function within other functions.

Expression line 1: f\left(x\right)=x^{2}+3x. Expression line 2: f\left(x\right)+2. Screenshot.

You can combine multiple functions together to create a separate function or you can create a composite function.

Expression line 1: f\left(x\right)=x^{2}+3x. Expression line 2: g\left(x\right)=5x^{3}. Expression line 3: h\left(x\right)=f\left(x\right)+g\left(x\right). Expression line 4: g\left(f\left(x\right)\right).  Screenshot.

You can use a function on points! This example scales the points by a factor of 2, and translates -2 units vertically. Explore this graph.

Expression line 1: f\left(z\right)=2\cdot z+\left(0,-2\right). Expression line 2: Table with coordinates for quadrilateral. Expression line 3: \operatorname{polygon}\left(\left(x_{1},y_{1}\right)\right). Expression line 4: \operatorname{polygon}\left(f\left(\left(x_{1},y_{1}\right)\right)\right).  Screenshot.

Learn More

Explore Functions Example Graph

Generalizing "for" Lists and Intervals

Lists

Polygons

Substitution

Tables

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