General Mathematics Introduction to Functions.pptx

LET’S 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)}

LET’S REVIEW
2. A person is earning ₱500.00 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. 𝑆(𝑛) = 500 + 𝑛
b. 𝑆(𝑛) =
500
𝑛
c. 𝑆(𝑛) = 500𝑛
d. 𝑆(𝑛) = 500 − 𝑛

LET’S REVIEW
3. A jeepney ride in Lucena costs ₱ 9.00 for the first
4 kilometers, and each additional kilometers adds
₱0.75 to the fare. Use a piecewise function to
represent the jeepney fare F in terms of the
distance d in kilometers.
a. 𝐹(𝑑) = {9 𝑖𝑓 0 > 𝑑 ≤ 4
b. 𝐹(𝑑) = {9 𝑖𝑓 0 < 𝑑 < 4
c. 𝐹(𝑑) = {9 𝑖𝑓 0 ≥ 𝑑 ≥ 4
d. 𝐹(𝑑) = {9 𝑖𝑓 0 < 𝑑 ≤ 4

LET’S REVIEW
4. Which of the following is the value of the
function 𝑓(𝑥) = 3𝑥2
− 15𝑥 + 5 + 3 given x
= 3?
a.25 c. 19
b.16 d. 10

LET’S REVIEW
5. Give the value of the of the function
𝑐(𝑥) = 5𝑥3
− 18 at 𝑐(3).
a.117 c. 153
b.27 d. 63

LET’S REVIEW
6. Given ℎ 𝑥 = 2𝑥2
− 7𝑥 and 𝑟 𝑥 =
𝑥2
+ 𝑥 − 1, find (ℎ + 𝑟)(𝑥).
a. 2𝑥2
– 1
b. 3𝑥2
+ 6𝑥 – 1
c. 3𝑥4
− 6𝑥2
– 1
d. 3𝑥2
− 6𝑥 – 1

LET’S REVIEW
7. Given ℎ 𝑥 = 𝑥 − 6 𝑎𝑛𝑑 𝑠 𝑥 = 𝑥2
−
13𝑥 + 42. Find
ℎ
𝑠
𝑥 .
a.
1
𝑥−7
b. 𝑥 − 7 c.
𝑥−6
𝑥−7
d. 𝑥 − 6

LET’S REVIEW
8. Given 𝑓 𝑥 = 6𝑥2
+ 7𝑥 + 2 and 𝑔(𝑥) =
5𝑥2
− 𝑥 − 1, find (𝑓 − 𝑔)(𝑥).
a. 𝑥2
+ 8𝑥 + 3
b. 5𝑥2
+ 8𝑥 – 1
c. 𝑥2
+ 6𝑥 – 1
d. 𝑥2
+ 8𝑥 − 1

LET’S 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.40℃
b.50℃
c.120℃
d.180℃

LET’S 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

REPRESENTING
REAL-LIFE SITUATIONS
USING FUNCTIONS

RELATION VS. FUNCTION
• 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.
• 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.

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)}

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

EXAMPLES
Domain Range
A.
B.
C.
a
b
c
x
y
x
y
a
b
c
Jana
Dona
Maya
c
Ken
Mark
Rey

LET’S 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.

LET’S 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

LET’S TRY THIS!
4. A user is charged ₱250.00 monthly for a
particular mobile plan, which includes
200 free text messages. Messages in
excess of 200 are charged ₱1.00 each.
Represent the monthly cost for text
messaging using the function t(m), where
m is the number of messages sent in a
month.

LET’S TRY THIS!
5. A certain chocolate bar costs
₱50.00 per piece. However, if you
buy more than 5 pieces they will
mark down the price to ₱48.00 per
piece. Use a piecewise function to
represent the cost in terms of the
number of chocolate bars bought.

TYPES OF FUNCTIONS
b
x
f 
)
( 7

y x
x
f 
)
( 2
)
2
( 
f n
n
x
a
x
a
x
a
a
y 



 ...
2
2
1
0
0
a1
a 2
a b
x
f 
)
( 7

y x
x
f 
)
( 2
)
2
( 
f n
n
x
a
x
a
x
a
a
y 



 ...
2
2
1
0
0
a1
a 2
a

LET’S TRY THIS!
Directions: Evaluate the following
functions.

PERFORMING THE
FUNDAMENTAL OPERATIONS
ON FUNCTIONS

SOLVING PROBLEMS
INVOLVING FUNCTIONS

REMEMBER THIS!
George Polya’s 4 – 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.

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.

EXAMPLES
Example 1: A proposed Light Rail Transit
System Line 1 (LRT-1) fare would charge
for the first four stations and ₱5.00 for each
additional station over the proposed fare.

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

EXAMPLES
Example 2: Lucena Network charges ₱450.00
monthly cable connection fee plus ₱130.00 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.

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?

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 ₱
9.00 for the first 4 kilometers and additional ₱0.50
for each additional kilometer. Express the jeepney
fare (F) as function of the number of kilometers (d)
that Xandria pays for the ride.

LEARNING TASK 1
2. A van rental charges ₱5,500.00 flat rate for
a whole-day tour in CALABARZON of 5
passengers and each additional passenger
added ₱500.00 to the tour fare. Express a
piecewise function to show to represent the
van rental in terms number of passenger n.

LEARNING TASK 1
Part II: Evaluate the following functions.
Write your solution on a separate paper.
1. 𝑔(𝑥) = 5𝑥 − 7; 𝑔(𝑥2
+ 1)
2. ℎ(𝑡) = 𝑥2 + 2𝑥 + 4; ℎ(2)
3. 𝑘(𝑥) =
3𝑥2−1
2𝑥+4
; 𝑘(−3)

LEARNING TASK 1
4. 𝑓(𝑥) = 2𝑥2
+ 5𝑥 − 9; 𝑓(5𝑥 − 2)
5. 𝑔(𝑝) = 4𝑝
; 𝑝 =
3
2

LEARNING TASK 1
Part III: Answer the following.
1.Given ℎ 𝑥 = 3𝑥2
+ 2𝑥 − 4, 𝑤ℎ𝑎𝑡 𝑖𝑠 ℎ 𝑥 − 3 ?
2.Given 𝑛 𝑥 = 𝑥 + 5 𝑎𝑛𝑑 𝑝 𝑥 = 𝑥2
+ 3𝑥 −
10, 𝑓𝑖𝑛𝑑:
a. 𝑛 − 𝑝 𝑥 + 3𝑝 𝑥
b.
𝑛 𝑥
𝑝 𝑥

LEARNING TASK 1
c. (𝑝 ∘ 𝑛)(𝑥)
3. Let 𝑚 𝑥 = 𝑥 + 3, 𝑛 𝑥 = 𝑥3
−
4, 𝑎𝑛𝑑 𝑝 𝑥 = 9𝑥 − 5, 𝑓𝑖𝑛𝑑 𝑚 ∘

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 ₱15,000.00.
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:

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

General Mathematics Introduction to Functions.pptx

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