Name ______________________________
Class __________ Date __________
Alg. 2 Unit 1b Study Guide
1. Write the equation of the horizontal and vertical lines through the point (4, -3).
2. Write the equation of the line with x-intercept at -4 and y-intercept at 3.
3.
A 15-year old tree is 3.75 in. in diameter. A 100 year old tree has a trunk that is 25 in. diameter.
a.
Use the information to find the rate of change of the growing tree trunk
b.
Write an equation to model the relationship between age of the tree and diameter.
c.
How old is a tree that has a 16 in. diameter?
Graph each function.
4. 3y = x − 6
5.
2x + y = 6
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
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
6. What are the three forms of a line? Name them and write the form.
a.
b.
c.
Write an equation for each line.
7. slope = 14 ; 4,3
( )
2
3
4
5
6
8. Through (0, 4) and (-2, 3)
Graph each system of inequalities. Show algebraically whether or not (1, -2) is a solution.
2 x − 3 y ≥ −6
 y > −2 x + 3
 x ≥ −4
 y − 2 < −x + 3
9. 
10. 
6
6
5
5
4
4
3
3
2
2
1
1
-6 -5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
-6
2
3
4
5
6
-6 -5 -4 -3 -2 -1
1
-1
-2
-3
-4
-5
-6
2
3
4
5
6
Name ______________________________
Class __________ Date __________
Write a piecewise function for each graph. Make sure to include the domain.
11.
12.
f(x)=
f(x)=
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
3
4
5
6
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
Graph each piecewise function.
−𝑥𝑥 + 3 𝑖𝑖𝑖𝑖 − 3 < 𝑥𝑥 < −1
14. 𝑓𝑓(𝑥𝑥) = � 3𝑥𝑥 + 1 𝑖𝑖𝑖𝑖 − 1 ≤ 𝑥𝑥 < 1
−4 𝑖𝑖𝑖𝑖 𝑥𝑥 ≥ 1
2𝑥𝑥 + 3 𝑖𝑖𝑖𝑖 − 3 < 𝑥𝑥 ≤ 1
13. 𝑓𝑓(𝑥𝑥) = �
5 𝑖𝑖𝑖𝑖 𝑥𝑥 > 1
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
3
4
5
6
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
Solve each system of equations using the specified method. WRITE YOUR ANSWER AS AN ORDERED PAIR!
15. Graphing
16. Substitution
17. Elimination
 − x + 2 y =6

−4
−4 x + y =
7
2 x − y =

10
3 x − 2 y =
−6
4 x + 3 y =

27
−5 x + 6 y =
Name ______________________________
Class __________ Date __________
1
1
Solve each system by any method.
3𝑥𝑥 − 𝑦𝑦 = 17
18. �
𝑦𝑦 + 2𝑥𝑥 = 8
𝑦𝑦 = 𝑥𝑥 + 3
20. �
𝑦𝑦 = −5𝑥𝑥 + 9
2𝑦𝑦 = −4𝑥𝑥
19.�
4𝑥𝑥 + 2𝑦𝑦 = −11
21. Suppose the drama club is planning a production that will cost $525 for the set and $150 per performance. A sold-out performance
will bring in $325. Write an equation for the cost C and an equation for the income I for p sold-out performances. How many
sold-out performances will it take for the club to break even?
22)
Suppose you are buying two kinds of notebooks for school. A spiral notebook costs $2, and a three-ring notebook costs $5. You
must have at least six notebooks. The cost of the notebooks can be no more than $20.
a.
Write a system of inequalities to model the situation.
Let x be the number of spiral notebooks and y be the number of 3-ring notebooks.
b.
Graph the system.
c. Would it work for you to buy just 7 spirals? Show why or why not algebraically.
Graph each system of constraints. Find all vertices. Evaluate the objective function at each vertex to find the maximum and
minimum value.
24.  x + y ≤ 6
23.  x + 2 y ≤ 6

x ≥ 2
y ≥1

Minimum for C = 3x +4y

2 x + y ≤ 10
 x ≥ 0, y ≥ 0

Maximum for P = 4x + y
Name ______________________________
Vertices: _______________________________________
Class __________ Date __________
Vertices: ____________________________________
Minimum: __________________
Maximum: _________________
25.
Suppose you make and sell lotion. A quart of regular skin lotion contains 2 c. oil and 1 c. cocoa butter. A quart of extra-rich
lotion contains 1 c. oil and 2 c. cocoa butter. You will make a profit of $10/qt on regular lotion and a profit of $8/qt on extrarich lotion. You have 24 c. oil and 18 c. butter. Write and graph a system of inequalities to model the situation and graph; let
x be the number of quarts of regular lotion, and let y be the number of quarts of extra-rich lotion. How many quarts of
each type of lotion should you make to maximize your profit? ***Hint: To accurately find your vertices, solve a system of
equations to find the intersection of your two boundaries.
Constraints:
Objective Function:
Vertices:
25b.
What is the maximum profit? What combination of lotions do you use to get the maximum profit?
26. Earnings A student can make a weekly salary of $200 plus 15% commission on sales at the Radio Barn or a weekly salary
of $300 plus 10% commission on sales at Woofer, Etc. For what amount of sales do these two jobs pay the same?
27. A manufacturer is producing entertainment units. Each TV unit costs $9 for parts and $15 for labor, and each Stereo Unit costs $6
and $20 for labor. The manufacturer’s budget is $810 for parts and $1800 for labor. To meet their production quota, they must make at
least 20 TV units and at least 30 stereo units. If the income per unit $150 for TVs and $175 for stereos, how many units of each should
be manufactured to maximize income?
Name ______________________________
Class __________ Date __________
Constraints:
Objective Function:
Vertices:
30.
What is the maximum income? What combination of units does the manufacturer need to make?