Section 9.1: Evaluating Radical Expressions and Graphing

Square Root and Cube Root Functions

9.1 Lecture Guide: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions

The natural number n is the index or the order of the radical.

Radical Notation

n x denotes the principal nth root of x

x is the radicand.

is the radical symbol, or the radical.

The natural number n is the index or the order of the radical.

Principal Square Root

Algebraically Verbally

Numerically

For any real number :

y x if 2y x and

0.y

x denotesthe principal square root of x.

Graphically

1,10,1 by 1,5,1

0x

Principal Cube Root

Algebraically Verbally

Numerically

For any real number x:

Graphically

3y x if y is a real number and 3 .y x

3 x denotesthe principal cube root of x.

27, 27,5 by 3, 3, 1

Objective: Evaluate radical expressions.

Evaluate each expression. Use a calculator only to check your answer.

1. 81 2. 3 27

Evaluate each expression. Use a calculator only to check your answer.

3. 4.4 81 3 27

Evaluate each expression. Use a calculator only to check your answer.

5. 6.4 16 3 125

Evaluate each expression. Use a calculator only to check your answer.

7. 9 16

Evaluate each expression. Use a calculator only to check your answer.

8. 9 16

Evaluate each expression. Use a calculator only to check your answer.

9. 9

16

Evaluate each expression. Use a calculator only to check your answer.

10.3

1

27

Objective: Graph square root and cube root functions.

11. 4f x x

Type:

x-intercept:

y-intercept:

Domain:

Range:

Table

4

3

0

5

x y

Graph

-10

10

-10 10

y

x

12.

Type:

x-intercept:

y-intercept:

Domain:

Range:

Table 3 1f x x

9

2

1

0

7

x y

Graph

-10

10

-10 10

y

x

Objective: Determine the domain of a square root function.

Domain of a Function y f x

The domain of a real-valued function y f x

set of all real numbers for which

is the

f x

____________________ ____________________ under a

is also a real

number. This means the domain excludes all values that

cause division by ____________________ or cause a

square root symbol.

13. Determine the domain of 2 5f x x

using a calculator. Then graph

without

1 2 5y x

a window of

using

5,5,1 by 5,5,1 to verify your result.

14. Determine the domain of

using a calculator. Then graph

without

a window of

using

5,5,1 by 5,5,1 to verify your result.

5 2f x x

1 5 2y x

Determine the domain of the following. Use a graphing calculator only as a check on your work.

15. 3 2 5f x x

Determine the domain of the following. Use a graphing calculator only as a check on your work.

16. 3

xf x

x

Determine the domain of the following. Use a graphing calculator only as a check on your work.

17. 2 8f x x

Determine the domain of the following. Use a graphing calculator only as a check on your work.

18. 2 3f x x

19. Given 3 2 5f x x evaluate each expression without a

calculator.

2f

11f

16f