Page 791 - Algebra 1

L E S S O N Graphing Square-Root Functions 114
Warm Up
1. Vocabulary Radicals that have the same radicands and roots such as
(69) 2√ 7 + 4√ 7 are ________, and radials that have different radicands and/or
roots such as 4√ 7 + 2√ 11 are ________. Add or subtract.
2. -6√ 2 + 8√ 2 (69)
Find each product.
4. (7 + √ 6)(4 - √ 9)
(76)
3. 31√5 - 13√ 5 (69)
5. (√ 3 - 12)2 (76)
New Concepts
The square root of a number x is the number whose square is x. √ 9=3 32=9
The square root of x can be a function. For the function y = √x when x is 9, y is 3 since the square root of 9 is 3. Use the table to make connections with the graph.
Math Language
A function is a mathematical relationship that pairs each value in the domain with exactly one value in the range.
x
y
0
0
1
1
4
2
9
3
16
4
y
6
4
2
O
x
4
8
1
2
Example
1
Hint
Try choosing x values that are perfect squares. This may make it easier to graph.
x
y
0
1
1
3
4
5
9
7
y
6
4
2
O
x
2
4
6
8
Online Connection www.SaxonMathResources.com
A square-root function is a function that contains a square root of a variable.
Graphing a Square-Root Function
Make a table of y = 2√x + 1. Then graph the function. SOLUTION
Evaluate the function when x is 0, 1, 4, and 9.
y = 2 √ 0 + 1 = 2 ( 0 ) + 1 = 1
y=2√ 1 +1=2(1)+1=3 y=2√ 4 +1=2(2)+1=5 y=2√ 9 +1=2(3)+1=7
In order for a square root to be a real number, the radicand cannot be negative.
776 Saxon Algebra 1