- The document discusses discrete and continuous domains in functions. A discrete domain is made up of distinct, unconnected points, while a continuous domain includes all numbers on the number line and makes connected lines or curves.
- One example shows a discrete function with domain values of 0, 1, 2, 3, 4, representing ticket prices. Another shows a continuous function for cheese prices with domain values from 0 to any fraction or decimal.
- Key differences are that discrete domains only include certain numbers while continuous domains include all numbers in the given interval.
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about functions and its operations such as addition, subtraction, multiplication, division and composition. It is also comprised of some examples and exercises to be done for the said topic.
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about functions and its operations such as addition, subtraction, multiplication, division and composition. It is also comprised of some examples and exercises to be done for the said topic.
Factor Theorem and Remainder Theorem. Mathematics10 Project under Mrs. Marissa De Ocampo. Prepared by Danielle Diva, Ronalie Mejos, Rafael Vallejos and Mark Lenon Dacir of 10- Einstein. CNSTHS.
Pre-Calculus Quarter 4 Exam
1
Name: _________________________
Score: ______ / ______
1. Find the indicated sum. Show your work.
2. Locate the foci of the ellipse. Show your work.
𝑥2
36
+
𝑦2
11
= 1
Pre-Calculus Quarter 4 Exam
2
3. Solve the system by the substitution method. Show your work.
2y - x = 5
x2 + y2 - 25 = 0
4. Graph the function. Then use your graph to find the indicated limit. You do not have to
provide the graph
f(x) = 5x - 3, f(x)
5. Use Gaussian elimination to find the complete solution to the system of equations, or state
that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
Pre-Calculus Quarter 4 Exam
3
6. Solve the system of equations using matrices. Use Gaussian elimination with back-
substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
7. A woman works out by running and swimming. When she runs, she burns 7 calories per
minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336
calories in her workout. Write an inequality that describes the situation. Let x represent the
number of minutes running and y the number of minutes swimming. Because x and y must be
positive, limit the boarders to quadrant I only.
Short Answer Questions: Type your answer below each question. Show your work.
8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that
each of these statements is true. Show your work.
Sn: 1
2
+ 4
2
+ 7
2
+ . . . + (3n - 2)
2
=
𝑛(6𝑛2−3𝑛−1)
2
Pre-Calculus Quarter 4 Exam
4
9. A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying
Sk+1 completely. Show your work.
Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3
10. Joely's Tea Shop, a store that specializes in tea blends, has available 45 pounds of A grade tea and
70 pounds of B grade tea. These will be blended into 1 pound packages as follows: A breakfast
blend that contains one third of a pound of A grade tea and two thirds of a pound of B grade tea
and an afternoon tea that contains one half pound of A grade tea and one half pound of B grade
tea. If Joely makes a profit of $1.50 on each pound of the breakfast blend and $2.00 profit on
each pound of the afternoon blend, how many pounds of each blend should she make to
maximize profits? What is the maximum profit?
11 Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86
and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a
$35 profit on each one. You expect to sell at least 100 laser printers this month and you need to
make at least $3850 profit on them. How many of what type of p
American public university math 110 complete courseChristina Walkar
Get help for American Public University MGT 656 New for all week assignments and discussions. We provide assignment, homework, discussions and case studies help for all subject American Public University for Session 2015-2016.
2. Adults $4.00
Children $2.00
8-2xyor1624 +==+ yx
Domain (x-values): 0, 1, 2, 3, 4
Range (y-values): 8, 6, 4, 2, 0
• The domain is discrete because it has
only the numbers 0, 1, 2, 3, and 4. Discrete
graphs are made up of distinct, or
unconnected, points.
• Since there is no such thing as half a
ticket, or one-forth of a ticket the domain
does not include those points between the
points graphed.
Functions shows a recipes mix of adult & children show
tickets.
3. 8-2xyor1624 +==+ yx
Domain (x-values): x ≥ 0 and x ≤ 0
(all numbers from 0 to 4)
Range (y-values): y ≥ 0 and y ≤ 8
(all numbers from 0 to 8)
• The domain is continuous because it
includes all numbers from 0 to 4 on the
number line. Continuous graphs are
made up connected lines or curves.
• Cheese can be divided into fractions
or decimals, so it is shown to be
continuous by using a line to include all
of those points.
Cheddar: $2/lb
Swiss: $4/lb
Functions shows a recipes mix of cheddar & Swiss cheese.
4. •Write a linear function to represent each problem.
•Graph the function.
•Describe the domain and range of each function. Is the
domain discrete or continuous?
You are in charge of reserving hotel rooms for a
baseball team. Each room costs $69, plus $6 tax, per
night. You need each room for two night. You need 10
to 16 rooms. Write a function for the total hotel costs.
yx =150
6. •Write a linear function to represent
each problem.
•Graph the function.
•Describe the domain and range of
each function. Is the domain discrete
or continuous?
The airline you are using for the
baseball trip needs an estimate
of the total weight of the team’s
luggage. You determine that
there will be 36 pieces of
luggage and each piece will
weigh from 25 to 45 pounds.
Write a function for the total
weight of the luggage.
1620or x4536x
900or x2536
≤⋅≤
≥⋅≥x
8. Key Idea
• A discrete domain is a set of input values that consists
of only certain numbers in an interval. Like integers 1
to 4.
• A continuous domain is a set of input values that
consists of all numbers in an interval. Like all numbers
1 to 4.
BACK
-3 -2 -1 0 1 2 3 4 5
-3 -2 -1 0 1 2 3 4 5
9. The graphs show the speeds of two cars over time.
Tell which graph corresponds to each situation.
Matching Situations to Graphs
Mr. Lee is traveling on the highway. He pulls over,
stops, then accelerates rapidly as he gets back on
the highway. Graph 2
10. The graphs show the speeds of two cars over time.
Tell which graph corresponds to each situation.
Matching Situations to Graphs
Ms. Montoni slows down as she leaves the main road. She
continues to slow down as she turns onto other streets
and eventually stops in front of her house. Graph 1
11. Check It Out: Example 1A
Tell which graph corresponds to the situation described
below.
Time
Runner’sSpeed
Time
Runner’sSpeed
Time
Runner’sSpeed
Graph 1 Graph 2 Graph 3
Jamie begins the race, and soon feels a pain in a
muscle. He is unable to complete the race.
Graph 2—Jamie is unable to complete the race, so his
speed decreases to zero.
12. Check It Out: Example 1B
Tell which graph corresponds to the situation described
below.
Time
Runner’sSpeed
Time
Runner’sSpeed
Time
Runner’sSpeed
Graph 1 Graph 2 Graph 3
Melissa builds up her speed during the beginning of the
race. She maintains her running speed for the
remainder of the race.
Graph 1—Melissa’s speed increases at the beginning
and then the graph remains constant.
13. Create a graph for the situation. Tell whether the graph is
continuous or discrete.
The table shows
the temperature
inside a car over
time.
Time 8:00 8:30 12:00 12:30
Temp.(F) 71 71 82 74
Car Temperature
64
66
68
70
72
74
76
78
80
82
84
8:00 8:30 12:00 12:30
Time
Temp(F)
Creating a Graph of a Situation
Since every value of
time has a
corresponding altitude,
connect the points.
The graph is continuous.
14. Create a graph for the situation. Tell whether the graph is
continuous or discrete.
A market sells pumpkins
for $5 each.
Pumpkin Cost
0
5
10
15
20
25
30
35
40
0 2 4 6 8
Pumpkins Purchased
Cost($)
Creating a Graph of a Situation
The cost (y-axis)
increases by $5 for each
pumpkin purchased (x-
axis).
Because each person can
only buy whole pumpkins
or none at all, the graph
is distinct points.
The graph is discrete.
15. Create a graph for the situation. Tell whether the graph is
continuous or discrete.
The table shows
the distance traveled
during a family vacation.
Distance Travelled
Example 2A
Since every value of
time has a
corresponding altitude,
connect the points.
The graph is continuous.
Time 8:00 10:00 12:00 2:00
Distance (mi) 280 320 500 580
0
100
200
300
400
500
600
700
8:00 10:00 12:00 2:00
Time
Distance(mi)
16. Lesson Quiz
Tell which graph corresponds to the situation. Then tell
whether the graph is continuous or discrete.
A bus pulls out from the gas station. It drives to its first stop.
Then the bus gets on the expressway.
Graph B; continuous
17. 1. Maggi has $25 in her bank account. She gets $5 every day
from her father and deposits the money in the account for
the first three days. On the fourth day, she buys a hat for
herself with the money. Identify the table that
corresponds to this situation.
A. B.
Lesson Quiz for Student Response Systems