Name: ______________________
Class: __________________
AU2: Notes #7 – Square & Cube Root Functions
Date: __________________
Warm Up:
Make a table for the following function and graph it: f x   2 x  2
y
x
f x   2 x  2
f x 
(x, f x  )
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
–2
–3
–4
Is this relation linear? Explain.
–5
–6
–7
–8
1
1
2
3
4
5
6
7
8
x
Example 1: Square Root Functions
Make a table and graph the square root function. f  x   x
y
f x  
x
10
x
9
0
1
4
9
16
25
8
7
6
5
4
3
2
Why does the domain and range
only include positive values?
1
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
x
–2
–3
How is f  x   x related to f x   x 2 ?
Example 2: Square Root Word Problem
For good weather conditions, police can use the formula r  2 5L to find the
approximate speed, r, of a car that leaves a skid mark of length, L, in feet. Complete the table and
graph the function.
y
L
0
5
20
45
80
r  2 5L
60
55
50
45
40
35
30
25
20
15
10
5
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
How long is the skid mark when the car’s speed when they hit the brakes was 60 mph?
2
x
Example 3: Transformations of square root functions.
Graph and label all four functions on the same coordinate plane below.
a) y  x  3
b) f x   x  3
y
10
9
8
7
6
5
4
3
2
1
–10 –9
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
x
–2
–3
–4
–5
–6
–7
–8
–9
–10
d) f  x   2 x
c) y  2 x
How are (a), (b), (c), and (d) related to f  x   x ? Explain.
3
Example 4: Cube Root Functions
Make a table and graph the cube root function. f  x   3 x
x
f x  
y
5
3
-27
-8
-1
0
1
8
27
x
4
3
2
1
–28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –8
–6
–4
–2
–1
2
4
6
8
10
12
14
16
18
20
22
24
26
28
x
–2
–3
–4
–5
Why does the domain also include negative values?
How is f  x   3 x related to f x   x 3 ?
Example 5: Cube Root Word Problem
Knowing the volume of a cube, V, the length of the cube’s edge, l, can be found using the
formula l  3 V . Make a table and graph the cube root function.
y
V
l 3V
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
Why does the domain not include negative values?
4
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
x
5