Transcript 10.1 1. 2. 3. 4. 5. 6. Radical Expressions and Functions Find the nth root of a number. Approximate roots using a calculator. Simplify radical expressions. Evaluate radical functions. Find the domain.

10.1
1.
2.
3.
4.
5.
6.
Radical Expressions and Functions
Find the nth root of a number.
Approximate roots using a calculator.
Simplify radical expressions.
Evaluate radical functions.
Find the domain of radical functions.
Solve applications involving radical functions.
Write as many perfect squares as you can.
Write as many perfect cubes as you can.
Rational expression
↔ fraction
Irrational expression
↔ radical
root or
index
radical
radicand
49
7
3
 25
= Not a real number 3
 27  3
 100  10

36  6

3
8
2
 125  5
5
32
2
64
3
125
4

5
Evaluating nth roots
• We CANNOT take an even root of a negative number.
4
4
 16
• We CAN take an odd root of a negative number.
3
 8  2
• If the index is even, there are 2 roots: one positive,
one negative.
The positive number is the principle root.
The radical symbol represents the positive root.
49
Rational expression
3
Irrational expression
Exact value
Approximate with calculator
3  1.732
Radical function: A function containing a radical
expression whose radicand has a variable.
Given f(x) = 5x  8, find f(3).
f  3  5  3  8  15  8  7
Graph.
f x  x
Domain:
0,  
The radicand must be greater than or equal to 0.
Find the domain.
f  x  x  8
x 8  0
x8
Domain: x | x  8
8,  
Find the domain.
f  x   3x  9
3x  9  0
3x  9
x3
Domain: x | x  3
 ,3
Find the domain of f(x) = 4 x  16 .
a)  x x  4 ,
or [4, )
b)  x x  4 ,
or [4, )
c)  x x  4 ,
or (, 4]
d)  x x  4 ,
or ( , 4]
Copyright © 2011 Pearson Education, Inc.
Slide 10- 11
Find the domain of f(x) = 4 x  16 .
a)  x x  4 ,
or [4, )
b)  x x  4 ,
or [4, )
c)  x x  4 ,
or (, 4]
d)  x x  4 ,
or ( , 4]
Copyright © 2011 Pearson Education, Inc.
Slide 10- 12