13-3 Graph Radical Functions
Name
Date
Graph y x 3 1. Find the domain and range of the function.
The domain has values of x such that x 3 0
x 3
Think
Choose values for x that make
the radicand a perfect square.
Make a function table.
y
x
y
x3 1
3
1
2
0
y
1
6
13
1
2
3
Graph the ordered pairs and draw smooth curves
to connect the points. The range is y 1.
The graph is translated 1 unit down and 3 units
to the left of the parent function y x.
7
6
5
4
3
2
1
ⴚ2 0
ⴚ1
x
2 4 6 8 10 12 14
On a separate sheet of paper, graph each radical function using a table. State the Check students’
tables and graphs.
domain and range. Describe how each graph relates to the graph of y ⴝ x.
1. y x5
2. y x ⴙ 5 ⱖ 0; x ⱖ ⴚ5
x 1 5 ⱖ 0; so y ⱖ 0
domain: x ⱖ ⴚ5; range: y ⱖ 0
The graph is translated 5 units to the left.
Copyright © by William H. Sadlier, Inc. All rights reserved.
3. y x6
5. y x 7
1
x 12
x3
domain: x ⱖ 0; range: y ⱖ ⴚ3
The graph is translated 3 units down.
8. y 1
domain: x ⱖ 0; range: y ⱖ 1
2
1
The graph is translated 1 units up.
2
x4
x ⴚ 4 ⱖ 0; x ⱖ 4
x ⴚ 4 ⱖ 0; so y ⱖ 0
domain: x ⱖ 4; range: y ⱖ 0
The graph is translated 4 units to the right.
6. y domain: x ⱖ 0; range: y ⱖ ⴚ7
The graph is translated 7 units down.
7. y x ⴙ 4 ⱖ 0; x ⱖ ⴚ4
x ⴙ 4 ⱖ 0; so y ⱖ 0
domain: x ⱖ ⴚ4; range: y ⱖ 0
The graph is translated 4 units to the left.
4. y x ⴚ 6 ⱖ 0; x ⱖ 6
x ⴚ 6 ⱖ 0; so y ⱖ 0
domain: x ⱖ 6; range: y ⱖ 0
The graph is translated 6 units to the right.
x4
1
x 32
1
domain: x ⱖ 0; range: y ⱖ 3
2
1
The graph is translated 3 units up.
2
Lesson 13-3, pages 336–337.
Chapter 13 335
For More Practice Go To:
On a separate sheet of paper, graph each radical function using a table. State the Check students’
tables and graphs.
domain and range. Describe how each graph relates to the graph of y ⴝ x.
9. y x9 2
10. y domain: x ⱖ ⴚ9; range: y ⱖ ⴚ2
The graph is translated 9 units to the left
and 2 units down.
11. y x6 7
13. y x 5 1.5
1
x4 2
1
2
The graph is translated 4 units to the left
1
and unit up.
2
domain: x ⱖ ⴚ4; range: y ⱖ
x3 6
domain: x ⱖ 3; range: y ⱖ 6
The graph is translated 3 units to the left
and 6 units up.
14. y domain: x ⱖ 5; range: y ⱖ ⴚ1.5
The graph is translated 5 units to the right
and 1.5 units down.
15. y domain: x ⱖ ⴚ3; range: y ⱖ ⴚ4
The graph is translated 3 units to the left
and 4 units down.
12. y domain: x ⱖ 6; range: y ⱖ 7
The graph is translated 6 units to the right
and 7 units up.
x3 4
x 9 2.5
domain: x ⱖ 9; range: y ⱖ ⴚ2.5
The graph is translated 9 units to the right
and 2.5 units down.
16. y 1
x 6 22
1
2
The graph is translated 6 units to the left
1
and 2 units up.
2
domain: x ⱖ ⴚ6; range: y ⱖ 2
Solve. Check students’ graphs.
Solve: x ⴝ x ⴙ 6 ; x2 ⴝ x ⴙ 6; x2 ⴚ x ⴚ 6 ⴝ 0
(x ⴚ 3)(x ⴙ 2) ⴝ 0; x ⴚ 3 ⴝ 0 or x ⴙ 2 ⴝ 0
(3, 3) or (ⴚ2, ⴚ2)
x ⴝ 3 or x ⴝ ⴚ2
Check by substitution:
for (3, 3):
for (ⴚ2, ⴚ2):
?
?
ⴚ2 ⴝ ⴚ2 ⴙ 6
3 ⴝ 3ⴙ6
3 ⴝ 3 True
ⴚ2 ⴝ 2 False
The only point of intersection is (3, 3).
18. Find the solution of the system y 2x and
y x 3. Check your answer by graphing
the equations on grid paper.
Solve: 2x ⴝ x ⴙ 3 ; 4x2 ⴝ x ⴙ 3; 4x2 ⴚ x ⴚ 3 ⴝ 0
(4x ⴙ 3)(x ⴚ 1) ⴝ 0; 4x ⴙ 3 ⴝ 0 or x ⴚ 1 ⴝ 0
3
x ⴝ ⴚ or x ⴝ 1. Check by substitution:
4
3
for x ⴝ 1:
for x ⴝ ⴚ :
4
?
?
3
3 3
ⴚ ⴝ 9 ; ⴚ ⴝ False
2 ⴝ 4 ; 2 ⴝ 2 True
2
2 2
4
The only point of intersection is (1, 2).
19. How do the graphs of y x and y 2 x differ? Test your observation
by replacing the coefficient of x with other values.
The domains and ranges for both functions are the same, but the y-values of the graph of y ⴝ 2 x
are greater than for the graph of y ⴝ x . Therefore, the greater the positive coefficient, the farther the
y-values of the graph are from the x-axis. The smaller the positive coefficient, the closer the y-values
of the graph are from the x-axis.
336 Chapter 13
Copyright © by William H. Sadlier, Inc. All rights reserved.
17. Find the solution of the system y x and
y x 6 and check. Then graph the
equations on a separate sheet of paper.