2. What we are about to learn…
a. Define functions, and piece-wise functions
b. Determine whether a relation is a function
or not;
c. Represent real-life situations using
functions, including piece-wise functions.
3. What will happen to the following if I’m
going to put this into this machine
(factory)?
1.Fish
2.Beef
What about if the machine will produce it
product using f(x) = x + 3
1.4
2.5
3.-2
4.
5. Functions
Functions relate an input to an
output
Functions in real life:
Output: Score in the test
Input: No. of hours studied
8. Functions
a. set of ordered pair
1. {(3,2), (4,0), (5,1), (2,3)} Function
2. {(1,2), (0,3), (1,6), (5,4)}
3. {(3,4), (3,0), (3,1), (3,3)}
4. {(4,2), (3,2), (6,2), (5,2)}
Not Function
Not Function
Function
9. Functions
a. set of ordered pair ( x, y )
x - First element Domain
y - Second Element Range
Independent variable
Dependent variable
18. Write a piece-wise function from the given problem.
A Doctor's fee is based on the length of time.
• Up to 6 minutes costs Php 300
• Over 6 to 15 minutes costs Php 500
• Over 15 minutes costs Php 500 plus Php 100 per minute
above 15 minutes
19. A. Determine if the following sets of ordered pairs, table of values,
and equations represents a function.
1.{(5,9), (0,-3), (3,1), (11,-7)}
2.{(apple, banana), (apple, guyabano), (apple, guava), (apple,
pineapple)}
3.f(x) = x4
4.x = y2
5. X 2 6 2 8
f(x) 4 8 9 10
20. B. Problem solving using piecewise function
A merchant sells rice at Php 45.00 a kilo. If however, a buyer
buys more than 150 kilos of rice, the merchant gives a 10%
discount.
1. If x represents the number of kilos of rice purchased,
express the amount to be paid by f(x).
2. How much should be paid for 100 kilos of rice?
3. How much should be paid for 200 kilos of rice?
21. A Function f is a correspondence between two sets, the
domain and the range, such that for each value in the
domain, there corresponds exactly one value in the
range.
A Piece-wise function is a function which consists of
two or more functions in a specified domain.
33. Functions
Assessment:
A. Which of the following are functions
1. {(4,3),(-4,3),(3,3)}
2. {(2,5),(4,4),(2,3)}
Function
Not Function
Not Function
Function
3. 4
.
Editor's Notes
What have you noticed with our inputs?
How did you identify the output in each input?
If 4 is our input in f(x) = x + 3 what will be the output? Is there possibility that we can get two output in 4?
Analysis:
Based on the activity, how did you determine that the given relation is function or not?
What concept did you used in finding the relation as a function or not?
What is the difference between a function and a piece-wise function?
