Families of Functions modular course

Deepen understanding of the family of functions with these video lessons. Here we'll investigate Linear Relations as well as explore 15 parent functions in detail, the unique properties of each one, how they are graphed and how to apply transformations.

Getting started

The sections below list the complete series of learning modules for each function family. Within each module, you'll find three video sections: the featured function, introductions to transformations, and quick graphing exercises. All are focused on helping students learn how to graph parent functions and their transformations.

Watch the short video to get started, and find out how to make the most of TI Families of Functions as your teaching resource.

Download the Quick Reference Guide for course videos and materials

Parent functions

How to graph this particular parent function (P)

Quick! Graph this particular parent function (Q)

Transformations

Dilations (D)

Vertical shifts (V)

Horizontal shifts (H)

Horizontal stretch/shrink (K)

The opposite of a function (S)

The function evaluated at the opposite of x (N)

Combining more than one transformation (C)

m00

Linear Relations
Ax+By=C

How to graph any linear relation in any form, in one or two variables.

Go to resource library

m01

Quadratic
y=x²

How to graph the quadratic parent function and transformations of the quadratic function.

Go to resource library

m02

Absolute Value
y=abs(x)

How to graph the absolute value parent function and transformations of the absolute value function.

Go to resource library

m03

Square root
y=√x

How to graph the square root parent function and transformations of the square root function.

Go to resource library

m04

One over x
y=1/x

How to graph the reciprocal parent function and transformations of the reciprocal function.

Go to resource library

m05

Cubic
y=x³

How to graph the cubic parent function and transformations of the cubic function.

Go to resource library

m06

Cube root
y=∛x

How to graph the cube root parent function and transformations of the cubic function.

Go to resource library

m07

Exponential base 2
y=2ͯ

How to graph an exponential parent function and transformations of the exponential function.

Go to resource library

m08

Exponential base 1/2
y=(½)ͯ

How to graph an exponential parent function and transformations of the exponential function.

Go to resource library

m09

Exponential base e
y=eͯ

How to graph an exponential parent function and transformations of the exponential function.

Go to resource library

m10

Natural log
y=ln(x)

How to graph the natural log parent function and transformations of the natural log function.

Go to resource library

m11

Semicircle
y=√(r²-x²)

How to graph the semicircle parent function and transformations of the semicircle function.

Go to resource library

m12

Greatest integer
y=[x]

How to graph the greatest integer parent function and transformations of the greatest integer function.

Go to resource library

m13

Piecewise
f(x)

How to graph transformations of a generic piecewise function.

Go to resource library

m14

Sine
y=sin(x)

How to graph the sine parent function and transformations of the sine function.

Go to resource library

m15

Cosine
y=cos(x)

How to graph the cosine parent function and transformations of the cosine function.

Go to resource library

Please revise your search criteria. Activities for the topic at the grade level you selected are not available.

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Families of Functions modular course

Getting started

Parent functions

Transformations

Linear RelationsAx+By=C

Quadraticy=x2

Absolute Valuey=abs(x)

Square root y=√x

One over xy=1/x

Cubicy=x3

Cube rooty=∛x

Exponential base 2y=2ͯ

Exponential base 1/2y=(½)ͯ

Exponential base ey=eͯ

Natural logy=ln(x)

Semicircley=√(r2-x2)

Greatest integery=[x]

Piecewisef(x)

Siney=sin(x)

Cosiney=cos(x)

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Linear Relations
Ax+By=C

Quadratic
y=x²

Absolute Value
y=abs(x)

Square root
y=√x

One over x
y=1/x

Cubic
y=x³

Cube root
y=∛x

Exponential base 2
y=2ͯ

Exponential base 1/2
y=(½)ͯ

Exponential base e
y=eͯ

Natural log
y=ln(x)

Semicircle
y=√(r²-x²)

Greatest integer
y=[x]

Piecewise
f(x)

Sine
y=sin(x)

Cosine
y=cos(x)