Graphing Square Root and Cube Root Functions

Don’t freak out…

• YOU learned the basics to graphing last chapter

• This is just reinforcement!

Where we see ‘em…

Cube root and square root

Parent Square Root

X/Y table

X Value Y Value

4

9

16

25

36

49

64

Parent Cube Root

X/Y table

X Value Y Value

8

27

64

-8

-27

-64

Translations

Translations

You tell me…

• What would placing a negative sign in front of the radical do?

• What would placing a number like 2 in front of the radical do?

Practice

Ex: Graphing Square Root Functions

• Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least four points on each.

a. 5 y x

• Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least three points on each.

b. 3 y x

Ex: Graphing Square Root Functions

• Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least four points on each.

c. 2 1 y x

Ex: Graphing Square Root Functions

• Graph the parent function of the square root function and the following function on the same graph. Tell what transformation were done to the square root parent function. Graph at least four points on each.

d. 2y x

Ex: Graphing Square Root Functions

Square Roots and nth roots

• When c≥0, the square root of c is the non negative solution of the equation x2=c

• Cube roots, fourth roots, and higher roots are defined as solutions of the equation xn=c

• These equations can be solve graphically by finding the x coordinate of the intersection points of y=xn and y=c

Solutions to nth roots

Review…

Evaluate in your calculator

• 401/5

• 2251/111

• Watch your parentheses

Rational Exponents

Simplify