Graphing Square Root and Cube Root

Functions

Section 7.5

WHAT YOU WILL LEARN:

1. How to graph square root and cube root functions.

2. How to use square root and cube root functions to find real-life quantities.

Some Basic “Root” Graphs

xy 3 xy

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

Graphs of Radical Functions

xy

• On the your calculator, graph:

• Now graph: 3 xy

Movement of Basic Graphs

xy

• Those were your basic square root and cube root graphs. Let’s see how we can move them around. Try each of the following on your calculator:

4

2

2

1

3

2

1

xy

xy

xy

xy

xy

xy

Movement on the X and Y Axes• What did you notice?

Now the Cube Root Function

2

3

2

1

2

2

1

3

3

3

3

3

3

xy

xy

xy

xy

xy

xy

• Below the cube root graph, graph the following:

Summary

khxay • To graph or follow these steps:

1. Sketch the basic graph

2. Shift the graph h units horizontally and k units vertically.

khxy 3

Example 1

31 xyGraph

x-10 -5 5 10

y

-10

-5

5

10

Example 2

123 xy• Graph

x-10 -5 5 10

y

-10

-5

5

10

Example 3

1233 xy• Graph

x-10 -5 5 10

y

-10

-5

5

10

Finding Domain and Range

123 xy

• Find the domain and range of the following:

A.

B. 1233 xy

A “Real” Example

rs 95.4

• At an amusement park a ride called the rotor is a cylindrical room that spins around. The riders stand against the circular wall. When the rotor reaches the necessary speed, the floor drops out and the centrifugal force keeps the riders pinned to the wall. The model that gives the speed s (in meters per second) necessary to keep a person pinned to the wall is:

• Where r is the radius of the rotor. Use a graphing calculator to estimate the radius of a rotor that spins at a speed of 8 meters per second.

Homework

page 434, 16, 18, 19-21 all, 22, 25, 32, 35