Review: Modeling and Reasoning Part 2
Algebra 2
Linear Programming: For each problem wire the constraints, objective function, graph the feasible region and
determine the optimal solution.
1. Toys-A-Go makes toys at Plant A and Plant B. Plant A needs to make a minimum of 1000 toy dump trucks and
fire engines. Plant B needs to make a minimum of 800 toy dump trucks and fire engines. Plant A can make 10 toy
dump trucks and 5 toy fire engines per hour. Plant B can produce 5 toy dump trucks and 15 toy fire engines per
hour. It costs $30 per hour to produce toy dump trucks and $35 per hour to operate produce toy fire engines.
How many hours should be spent on each toy in order to minimize cost? What is the minimum cost?
2. The Cruiser Bicycle Company makes two styles of bicycles: the Traveler, which sells for $300, and the Tourister,
which sells $600. Each bicycle has the same frame and tires, but the assembly and painting time required for the
Traveler is only 1 hour, while it is 3 hours for the Tourister. There are 300 frames and 360 hours of labor
available for production. How many bicycles of each model should be produced to maximize revenue?
Piecewise functions:
Evaluate
3. 𝑓(3) =
4. ℎ(−8) =
5. ℎ(−2) =
6. 𝑓(2) =
7.𝑓(−5) =
8.ℎ(6) =
Graph the piecewise function:
𝑥 + 3, 𝑖𝑓 𝑥 ≤ −2
2,
9. 𝑔(𝑥) = { 𝑖𝑓 − 2 < 𝑥 < 1
−2𝑥 + 1, 𝑖𝑓 𝑥 ≥ 1
−3, 𝑖𝑓 𝑥 < −3
10. . ℎ(𝑥) = {𝑥 , 𝑖𝑓 − 3 ≤ 𝑥 ≤ 0
𝑥 − 4, 𝑖𝑓 𝑥 > 0
2
Transformations:
Using the given graph f(x): Complete the missing parts of the table below
Function notation
Description:
Graph:
11. y = f(-x)
12. y= f(x-2)-4
13.
Translate up 1 and left 2
14 Match each equation with the corresponding descriptions
A.
B.
C.
D.
E.
.
𝑓(𝑥) = −|𝑥| + 2
𝑓(𝑥) = −|𝑥 + 2|
𝑓(𝑥) = −|𝑥 − 2|
𝑓(𝑥) = |−𝑥| − 2
𝑓(𝑥) = |𝑥 + 2| + 2
a)
b)
c)
d)
e)
left 2 and Up 2
Reflect over y axis and down 2
Left 2 and reflect over x-axis
Right 2 and reflect over x-axis
Reflect over x-axis and up 2
Graph the given absolute value functions.
15.𝑦 = |𝑥 − 5| − 3
16. 𝑦 = 3|𝑥 + 2| + 1
Answers:
1.
2.
3.
𝑓(3) = 5
4.ℎ(−8) = −5
5. ℎ(−2) = 4
6. 𝑓(2) = 5
7. 𝑓(−5) = 26
8. ℎ(6) = −4
9.
11. Reflect over y-axis
14. A ( e); B (c); C(d);
15.
10
12. Right 2 down 4
D(b); E(a)
16.
13. 𝑓(𝑥 + 2) + 1