Unit 2 Practice Test
Algebra II
READ THIS: You asked for more problems, so I gave them to you. Remember that you
don’t have to complete every problem. Spend your time working on those that you need
practice with.
Important Questions:
When is the test? When does Mr. Clithero stay after school?
Can use Desmos on the test? Can you use a graphing calculator?
What is a function?
How do you determine if a function is linear from the graph, the rule, or the table?
What do the graphs of each parent function look like?
What is modeling?
Transformation
Horizontal
Vertical
Fill in the table.
Reflection (flip)
Translation
(slide)
Stretch or shrink
For two-variable inequality graphs, what does the shading represent?
Vocab:
equation, relation, function, input, output, domain, range, linear, slope, y-intercept, slopeintercept from, point-slope form, parallel, perpendicular, direct variation, linear modeling,
quadratic, cubic, square root, absolute value, exponential, rational, transformation, translation
(slide), reflection (flip), stretch, shrink, inequality, include, exclude, solution
Review Questions:
2.1 Relations and Functions
1. What is the Vertical Line Test?
2. Give an example of a relation that is not a function for a table, graph and mapping
diagram.
3. Give an example of a function for a table, graph and mapping diagram.
4. Give the domain and range for one of the tables below.
5. Give the domain and range for the quadratic parent function.
6. Give the domain and range for cubic parent function.
7. Give the domain and range for the square root parent function.
8. Find the rule (the last row is hard)
x
y
x
f(x)
x
y
-3
-2
-1
0
1
2
8
9
10
11
12
13
-6
-1
0
2
3
5
23
8
5
-1
-4
-10
-7
11
½
4
0
-2.1
42
114
-6.75
9
-7
-2/59
x
g(x)
x
y
x
k(x)
-9
-7
-5
-3
-1
1
10
6
2
2
6
10
57/16
11
102
1
2
18
1.25
3
10
undefined
0
4
-2
6
4
-1
2
10
¼
64
16
½
4
1024
2.2 Linear Equations
9. Graph y = -4x +3
10. Graph y = 3x – 5
11. Graph y = 2/3x +2
12. Graph y = -1/4x -7
13. What is the purpose of sliders using Desmos for m and b when you have y = mx + b ?
14. Do the tables represent linear functions?
x
g(x)
x
y
x
k(x)
-4
-2
0
2
4
6
8
10
12
14
18
20
15
9
-6
6
0
12
2
-2
-12
-4
-8
0
-12
0
4
8
-12
-4
2
5
6
7
2
3
15. What is the formula for slope?
16. What is the point-slope formula? What information do you need to use this formula?
What does the formula give you?
17. Parallel lines have slopes that are _________________.
18. Perpendicular lines have slopes that are ________________________.
19. Find the equation of the line that has a m = ¾ and passes through the point (-4,5).
20. Find the equation of the line that has a m = -5 and passes through the point (8,0).
21. Find the equation of the line that has passes through the points (0,4) and (-2,0).
22. Find the equation of the line that has passes through the points (-4,-4) and (0,3).
23. Find the equation of the line that passes through (3,-5) and is parallel to y = ½ x + 9.
24. Find the equation of the line that passes through (-6,8) and is perpendicular to y = ½ x+9.
25. Draw two lines that are parallel. Draw two lines that are perpendicular.
2.3 Direct Variation
26. What is the formula that models all direct variations? What is the y-intercept for all direct
variations?
27. Determine if the relations below are direct variations. If they are direct, then find k.
x
g(x)
x
y
x
k(x)
11
3
-5
½
0.46
298
66
18
-3
3
2.76
1788
45
18
5/3
2.99
-7
0
33.75
13.5
1.25
2.2
-5
0
1000
100
10
1
1/10
1/100
27300
2730
273
27.3
2.73
0.273
2.4 Linear Modeling
28. There is a pizza place in Chicago called Debonairs, they are famous for huge, Chicagostyle pieces of pizza. Your first piece costs $8.00. The second piece costs $7.50. The third,
$7.00, and so on. Create a linear equation that models the price for any piece of pizza.
Define the variables.
29. Find the cost of pizza for you and five friends at Debonairs.
30. Franklin sells magazines to raise money for his hockey club team. For a one-time price
of only $28.75, customers can subscribe to magazines for $5 each. Create a linear equation
that models the total cost for any number of magazine subscriptions. Define the variables.
31. Find the cost for ordering Time, Sports Illustrated and GQ.
32. It is 603 miles from Pittsburgh to St. Louis. The Cardinals leave Pittsburgh for St. Louis
at 1:30 AM on Tuesday. Their plane travels at average speed of 230 mph. Create a linear
equation that models the distance the Cardinals are from St. Louis. Define the variables.
33. How are Cardinals from St. Louis at 2:45 AM on Tuesday? What is a reasonable domain
and range for the equation your created?
34. Below is a table showing data collected in various countries that represent a countries
entrepreneurship capabilities and student’s math scores. Use Desmos to create a scatter
plot of the data and find the line of best fit. Write the equation for the line of best fit.
Greece
United States
Germany
United Kingdom
France
Korea
Singapore
Switzerland
Entrepreneurship
Capabilities
49.7
55.7
37.1
42.5
38.4
26.7
24.1
42.4
Math Scores
466
487
513
492
497
546
562
543
http://zhaolearning.com/2012/06/06/test-scores-vs-entrepreneurship-pisa-timss-and-confidence/
2.5 Absolute Value Functions and Graphs
*problems from this section are mixed into the other sections
2.6 Parent Functions (Families of Functions) and Transformations
35. Determine the parent function from the rule.
y  mx  b
y  ( x  84)  4
4
5
2
h( x ) 
1
x9
g ( x)  6 x 3  9
y  74 x 3
k ( x )  5 x  2
f ( x)   x 2  8
y  5x 8
a ( x)  1593  1
x
y  y1  m( x  x1 )
w( x)  x 3  x 2  x  1
.4
j ( x)  13.52 x  903
45  99.34 x
y   12 
x 1
y  8x  1
h( r )   r  3
y   x 8 9
$(t )  10,000  (1.05) t
h(t )  h0  vo t  12 at 2
1
y   2
 x
5
C  9 ( F  32)
v(t )  v0  at
F  95 C  32
p(d )  r 3  d 2
2
3
p(r )  r 3  d 2
36. Determine the parent function from the graph.
37. Determine the parent function from the table.
x
h(x)
x
y
x
y
-1
3
-5
2
0
6
-1
27
-125
8
0
216
8
-9
45
-92
0
-15/6
8
9
45
92
0
15/6
1
6
1.2
-2
0
-9
1
36
1.44
4
0
81
x
y
t
d(t)
x
m(x)
81
1
0
256
25
100
9
1
0
16
5
10
-11
4
73
2/4
-5.2
0
-11
4
73
2/3
-5.2
0
-2
-1
0
1
2
3
1/9
1/3
1
3
9
27
x
p(x)
x
y
x
y)
10
6
-8
0
1
2
0.1
1/6
-1/8
ERR
1
1/2
6
9
-1
1
2
7
27
66
6
2
3
38
-1
0
1
-2
2
1
1
1
?
?
38. Describe the transformations. Write the rule.
39. Describe the transformations. Create a graph.
y  ( x  3) 2  1
y  x2  4
y x
f ( x)  2 x 3
g ( x )  3 x  6
1
x
y  13 x  2
y
2.7 Two Variable Inequalities
40. How are open and closed circles related to dashed and solid lines?
41. For two-variable inequality graphs, when is the graph shaded up or down?
42. Graph
y x 4
y  12 x  2
f ( x)   x 2  5
y   x  3 1