Name ______________________________
Class __________ Date __________
Algebra II ~ Chapter 2 Study Guide
Find the domain and range of each relation, and determine whether it is a function.
1. {(2, 1), (-4, 5), (1, 7), (2, -3), (-1, 2)} Function Y/N _____ Domain ____________
Range ____________
2.
{(1, -1), (2, -2), (3, -3), (4, -4), (5, -5)} Function Y/N _____ Domain ____________
Range ____________
3.
Draw a mapping diagram for the relation {(-3, 2), (-1, 0), (1, 2), (3 ,4)}. Is the relation a function? Explain.
Function Y/N _____
Suppose f(x) = 3x – 4 and g(x) = |x| + 3. Find each value.
4.
f 2
5.
f (1)
g (1)
Find the constant of variation for the direct variation problem. Then find the value of y when x =
6.
y = 2 when x = 6
7.
The diameter of a tree varies directly as its age. A 15-year old tree is 3.75 in. in diameter.
How old will the tree be when it is 25 in. in diameter?
Find the slope of each line.
8. 3x – 5y = 15
9. through (-2, 7) and (4, 1)
3
4
10. through (6, 1) and perpendicular to
.
y  32 x  14
Name ______________________________
Graph each function.
10. y  12 x  1
Class __________ Date __________
12. y  | x  2 | - 3
6
6
5
5
4
4
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
1
2
3
4
5
6
-6 -5 -4 -3 -2 -1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
13. y  - | x |  4
1
2
3
4
5
6
1
2
3
4
5
6
14. y  3 - 2x
6
6
5
5
4
4
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
1
2
3
4
5
6
-6 -5 -4 -3 -2 -1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
Write in standard form the equation of the line with the given slope through the given point.
15. slope = 6; 12 ,2
16. slope = 14 ; 4,3
 
Write in point-slope form, then change to slope-intercept form.
17. (0, 0) and (-2, 3)
18. (-4, 1) and (-2, -2)
point-slope ______________________________
point slope __________________________________
slope-intercept _______________________
slope-intercept _____________________________
Name ______________________________
Class __________ Date __________
19. The table below displays the enrollment at Westside High during the years 1996-2001.
Year
Enrollment (in hundreds)
0
9
1
11
2
12
3
14
4
15
a. Make a scatter plot of the data
b. Use a graphing utility to find the line of best fit for the data.
DRAW the trend line on the graph to the right (be accurate).
WRITE the equation for the trend line below.
c.
Estimate the enrollment in 6 years.
Describe each translation of y = |x| as vertical, horizontal, or combined.
Then graph each translation.
20. y | x | 2
21. y | x  4 |
Translation ____________________________
Translation ____________________________
6
6
5
5
4
4
3
3
2
2
1
-6 -5 -4 -3 -2 -1
1
1
2
3
4
5
6
-6 -5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
Graph each inequality.
23. y  2 x  3
3
4
5
6
2
3
4
5
6
24. 2 x  3 y  6
6
6
5
5
4
4
3
3
2
2
1
-6 -5 -4 -3 -2 -1
2
1
1
2
3
4
5
6
-6 -5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
Write an equation for each function.
25. ________________________
-4
26. _________________________
27. _______________________
4
4
4
2
2
2
-2
2
4
-4
-2
2
4
-4
-2
2
-2
-2
-2
-4
-4
-4
4