4/30/2014
Given the graph of the function find the following:
8.1 Radical Functions
Given the function f ( x)  3.2 6 x find the following:
a. Estimate g
 2
a. f (45)
b. Estimate x such that g ( x )
 9
b. Estimate x such that f ( x)  16
Back to Table of Contents
8.1‐3
Give the domain and range of the following radical functions.
a. g ( x)  7 x  5
c. f ( x)  8  x
Back to Table of Contents
8.1‐3
Give the domain and range of the following radical functions.
a. h( x)  x  10
b. Back to Table of Contents
8.1‐4
Back to Table of Contents
8.1‐5
1
4/30/2014
Give the domain and range of the following radical functions.
b. 3.1 Exponents revisited
Radical expression can also be written with rational (fraction) exponents.
⁄
In general: Examples:
a. ⁄
______
⁄
Similarly: b. = _____
b. = _____
OR Examples:
a. ⁄
______
6
Back to Table of Contents
8.1‐5
Rewrite the following exponents in radical form.
1
a. b. a4
3
5
p
1
2 8 2
a. 81m n

Rewrite the following radicals using rational exponents.
6x
c. d. 7
Simplify the following expressions. Write all answers without negative exponents. 1
 32 x5 y10 z 1  4
b. 
 2 xy 2 z 3 


h2
Back to Table of Contents

3.1‐7
Back to Table of Contents
3.1‐9
2
4/30/2014
Simplify the following radicals. Assume all variables are nonnegative.
8.2 Simplifying, Adding, and Subtracting Radicals
b.
3
343
c.
3
64
5
32
d.
36m 2
a. Evaluate the following radicals without a calculator.
a. 4
b. 3
54g 4 h11
9
Back to Table of Contents
Add or subtract the following expressions. Assume all variables are nonnegative.
a. 5 64 6
b. Add or subtract the following expressions. Assume all variables are nonnegative.
7ab 2 7ab  4a 63ab5
a. b. Back to Table of Contents
8.2‐2
8.2‐3
8 3a  4 5 3a  2 3a  17 5 3a
4
32m5 n6  3 5 2mn 2  5mn 4 2mn 2
Back to Table of Contents
8.2‐4
3
4/30/2014
Multiply the following and simplify the result.
8.3 Multiply and Divide Radicals
a. 3a  5b
b.
6m  10m
c. 3
a. b. (3 
5) 2
6a  3 12a 2
Back to Table of Contents
16
25
b. Back to Table of Contents
8.3‐1
Simplify the following radicals. a. (2  11)(8  5)
8.3‐3
Rationalize the denominator and simplify the following radical expressions. 50a 5b3
8ab7
a. Back to Table of Contents
8.3‐4
7
6
b. 3a
5b
Back to Table of Contents
8.3‐5
4
4/30/2014
Rationalize the denominator of the following fractions.
a. 6
5 2
b. 47 2
5 6
Back to Table of Contents
8.3‐7
5