โOh GOSH! Reflecting on Hackteria's Collaborative Practices in a Global Do-It...
ย
General Mathematics Introduction to Functions.pptx
1. LETโS REVIEW
1. Which of the following relations is/are
function/s?
a. x = {(1,2), (3,4), (1,7), (5,1)}
b. g = {(3,2), (2,1), (8,2), (5,7)}
c. h = {(4,1), (2,3), (2, 6), (7, 2)}
d. y = {(2,9), (3,4), (9,2), (6,7)}
2. LETโS REVIEW
2. A person is earning โฑ500.00 per day for doing a
certain job. Which of the following expresses
the total salary S as a function of the number n
of days that the person works?
a. ๐(๐) = 500 + ๐
b. ๐(๐) =
500
๐
c. ๐(๐) = 500๐
d. ๐(๐) = 500 โ ๐
3. LETโS REVIEW
3. A jeepney ride in Lucena costs โฑ 9.00 for the first
4 kilometers, and each additional kilometers adds
โฑ0.75 to the fare. Use a piecewise function to
represent the jeepney fare F in terms of the
distance d in kilometers.
a. ๐น(๐) = {9 ๐๐ 0 > ๐ โค 4
b. ๐น(๐) = {9 ๐๐ 0 < ๐ < 4
c. ๐น(๐) = {9 ๐๐ 0 โฅ ๐ โฅ 4
d. ๐น(๐) = {9 ๐๐ 0 < ๐ โค 4
4. LETโS REVIEW
4. Which of the following is the value of the
function ๐(๐ฅ) = 3๐ฅ2
โ 15๐ฅ + 5 + 3 given x
= 3?
a.25 c. 19
b.16 d. 10
5. LETโS REVIEW
5. Give the value of the of the function
๐(๐ฅ) = 5๐ฅ3
โ 18 at ๐(3).
a.117 c. 153
b.27 d. 63
6. LETโS REVIEW
6. Given โ ๐ฅ = 2๐ฅ2
โ 7๐ฅ and ๐ ๐ฅ =
๐ฅ2
+ ๐ฅ โ 1, find (โ + ๐)(๐ฅ).
a. 2๐ฅ2
โ 1
b. 3๐ฅ2
+ 6๐ฅ โ 1
c. 3๐ฅ4
โ 6๐ฅ2
โ 1
d. 3๐ฅ2
โ 6๐ฅ โ 1
7. LETโS REVIEW
7. Given โ ๐ฅ = ๐ฅ โ 6 ๐๐๐ ๐ ๐ฅ = ๐ฅ2
โ
13๐ฅ + 42. Find
โ
๐
๐ฅ .
a.
1
๐ฅโ7
b. ๐ฅ โ 7 c.
๐ฅโ6
๐ฅโ7
d. ๐ฅ โ 6
8. LETโS REVIEW
8. Given ๐ ๐ฅ = 6๐ฅ2
+ 7๐ฅ + 2 and ๐(๐ฅ) =
5๐ฅ2
โ ๐ฅ โ 1, find (๐ โ ๐)(๐ฅ).
a. ๐ฅ2
+ 8๐ฅ + 3
b. 5๐ฅ2
+ 8๐ฅ โ 1
c. ๐ฅ2
+ 6๐ฅ โ 1
d. ๐ฅ2
+ 8๐ฅ โ 1
9. LETโS REVIEW
9. If the temperature in degrees Celsius inside
the Earth is represented by T(d) = 10d + 20
where (d) is the depth in kilometers, what is the
temperature inside the Earth in 10 kilometers?
a.40โ
b.50โ
c.120โ
d.180โ
10. LETโS REVIEW
Cotta National High School has 1,200 students enrolled in
2016 and 1,500 students in 2019. The student population
P grows as a linear function of time (t), where t is the
number of years after 2016. How many students will be
enrolled in Cotta National High School by 2020?
a.1,800
b.1,700
c.1,600
d.1,650
12. RELATION VS. FUNCTION
โข A relation is any set of ordered pairs. The set of all first
elements of the ordered pairs is called the domain of the
relation, and the set of all second elements is called the
range.
โข A function is a relation or rule of correspondence
between two elements (domain and range) such that
each element in the domain corresponds to exactly one
element in the range.
13. EXAMPLES
Given the following, which relations are
functions?
A = {(1,2), (2,3), (3,4), (4,5)}
B = {(3,3), (4,4), (5,5), (6,6)}
C = {(1,0), (0, 1, (-1,0), (0,-1)}
D = {(a,b), (b, c), (c,d), (a,d)}
14. EXAMPLES
x 1 2 3 4 5 6
y 2 4 6 8 10 12
x 4 -3 1 2 5
y -5 -2 -2 -2 0
x 0 -1 4 2 -1
y 3 4 0 -1 1
17. LETโS TRY THIS!
Directions: Try to create equations using
the following situations.
1. If height (H) is a function of age (a),
a function H that can represent the
height of a person in a age, if every
the height is added by 2 inches.
18. LETโS TRY THIS!
2. If distance (D) is a function of time (t), give
a function D that can represent the distance
a car travels in t time, if every hour the car
travels 60 kilometers.
3. Give a function B that can represent the
amount of battery charge of a cellular
phone in h hour, if 12% of battery was loss
every hour
19. LETโS TRY THIS!
4. A user is charged โฑ250.00 monthly for a
particular mobile plan, which includes
200 free text messages. Messages in
excess of 200 are charged โฑ1.00 each.
Represent the monthly cost for text
messaging using the function t(m), where
m is the number of messages sent in a
month.
20. LETโS TRY THIS!
5. A certain chocolate bar costs
โฑ50.00 per piece. However, if you
buy more than 5 pieces they will
mark down the price to โฑ48.00 per
piece. Use a piecewise function to
represent the cost in terms of the
number of chocolate bars bought.
22. TYPES OF FUNCTIONS
b
x
f ๏ฝ
)
( 7
๏ฝ
y x
x
f ๏ฝ
)
( 2
)
2
( ๏ฝ
f n
n
x
a
x
a
x
a
a
y ๏ซ
๏ซ
๏ซ
๏ซ
๏ฝ ...
2
2
1
0
0
a1
a 2
a b
x
f ๏ฝ
)
( 7
๏ฝ
y x
x
f ๏ฝ
)
( 2
)
2
( ๏ฝ
f n
n
x
a
x
a
x
a
a
y ๏ซ
๏ซ
๏ซ
๏ซ
๏ฝ ...
2
2
1
0
0
a1
a 2
a
33. REMEMBER THIS!
George Polyaโs 4 โ Step Rule
1. Explore. This step involves careful reading,
analyzing, identifying the given and unknown
the problem and expressing the unknown in terms
variables.
2. Plan. In this step writing an equation that
describes the relationships between or among the
variables is involve.
34. REMEMBER THIS!
3. Solve. This step requires working out with the
written equation and other number relations to
determine the required quantities that answer the
question in the problem.
4. Check. The final step that employ the use of other
approaches to examine the appropriateness of the
answer.
35. EXAMPLES
Example 1: A proposed Light Rail Transit
System Line 1 (LRT-1) fare would charge
for the first four stations and โฑ5.00 for each
additional station over the proposed fare.
36. EXAMPLES
a.Find the fare function f(x) where x represents
the number of stations traveled
b.Find the proposed fare for 15 stations
c.Find the proposed fare for 20 stations
37. EXAMPLES
Example 2: Lucena Network charges โฑ450.00
monthly cable connection fee plus โฑ130.00 for
each hour of pay-per-view (PPV) event
regardless of a full hour or a fraction of an
a.Find payment function f(x) where x
the number of PPV hours.
38. EXAMPLES
b. What is the monthly bill of a customer who
watched 25 hours of PPV events?
c. What is the monthly bill of a customer who
watched 0.5 hour of PPV events?
39. LEARNING TASK 1
Part I: Read each situation carefully to solve each
problem. Write your answer on a separate sheet of
your paper.
1.Xandria rides through a jeepney which charges โฑ
9.00 for the first 4 kilometers and additional โฑ0.50
for each additional kilometer. Express the jeepney
fare (F) as function of the number of kilometers (d)
that Xandria pays for the ride.
40. LEARNING TASK 1
2. A van rental charges โฑ5,500.00 flat rate for
a whole-day tour in CALABARZON of 5
passengers and each additional passenger
added โฑ500.00 to the tour fare. Express a
piecewise function to show to represent the
van rental in terms number of passenger n.
41. LEARNING TASK 1
Part II: Evaluate the following functions.
Write your solution on a separate paper.
1. ๐(๐ฅ) = 5๐ฅ โ 7; ๐(๐ฅ2
+ 1)
2. โ(๐ก) = ๐ฅ2 + 2๐ฅ + 4; โ(2)
3. ๐(๐ฅ) =
3๐ฅ2โ1
2๐ฅ+4
; ๐(โ3)
45. ASSIGNMENT
You wanted to join a booth fair, and you are
aiming to get a profit that is twice as your
capital. Your starting capital is โฑ15,000.00.
Make a financial plan for the booth that you
will set up and the product that you will sell.
You may use the sample plan below:
47. ASSIGNMENT
Categories Excellent
3
Fair
2
Poor
1
Budgeting Excellent
understanding in
creating a plan for
spending the money
Some understanding
in creating a plan for
spending the money
Little to no
understanding in
creating a plan for
spending the money
Planning The goal set is
achievable and
realistic
The goal set is hard
to achieve
The goal set is not
achievable and not
realistic
Accuracy of Solution The computation in
obtaining the desired
profit using the profit
function is correct
The computation in
obtaining the desired
profit using the profit
function has flaws
There is no attempt
in computing the
desired profit using
the profit function