general mathematics quarter 1 module 11, Study notes of Mathematics

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General Mathematics

General Mathematics

Quarter 1 – Module 1 1 :

One-to-One-Functions

What I Need to Know

This module was designed and written with you in mind. It is here to help you to assess your knowledge of the different mathematics concepts previously studied and your skills in performing mathematical problems. These knowledge and skills will help you understand one-to-one functions. As you go through this lesson, think of this important question: “ How one-to-one functions represents real life situations”? To find answer, read and perform each activity. In this module, the learners are expected to demonstrate understanding of key concepts of inverse functions, exponential functions, and logarithmic functions. Learners should also be able to apply concepts of inverse functions, exponential functions, and logarithmic functions to formulate and solve real-life problems with precision and accuracy. The module

• Lesson 1 – One-to-One Functions After going through this module, you are expected to:

1. determine if a function is a one-to-one.

2. identify real-life situation using one-to-one function.

What I Know

Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.

1. It is a rule which associates each element of set A with at least one element in set B. a. Function c. Set b. Relation d. Subset
2. It is a rule which uniquely associates elements of one set A with the elements of another set B; each element in set A maps to a single element in set B. a. Function c. Set b. Relation d. Subset

3. It associates two or more values of the independent (input) variable with a single value of the dependent (output) variable. a. One-to-one c. Many-to-one b. One-to-many d. Many-to-many
4. It is a single x-value that relates to two different y-values. a. One-to-one c. Many-to-one b. One-to-many d. Many-to-many
5. A single x-value relates to only one unique y-values. a. One-to-one c. Many-to-one b. One-to-many d. Many-to-many
6. Mabuhay National High School has its own School ID which is 143142 while other school also has their own school ID. Which rule represent the given statement? a. One-to-one c. Many-to-one b. One-to-many d. Many-to-many
7. Which of the following does not represent one-to-one function? a. My father to its child. b. Facebook name to password. c. Student’s Name to Learner’s Reference number (LRN). d. Cellphone Number to the owner.
8. Which of the following table of values represent one-to-one function? a. c. b. d. x y a b b c d e Wife Husband Raiza Anthony Mitchie Jeff Sarah Jordan x y

• 4 17
• 2 5 0 1 2 5 6 17 x y Klara Iphone Kath Iphone Loraine Samsung Ana Vivo

12. Functions can be written as _____________. a. ordered pairs b. tables c. graphs d. all of the choices
13. Let A = {1 0 , 2 0 , 30} and B = {Pandesal, Yema Cake, Mamon, Ensaymada}. Which of the following is a one-to-one function? a. {( 10 ,pandesal),( 20 ,Mamon), ( 30 ,Pandesal)} b. {( 10 ,Yema Cake), ( 20 ,Ensaymada), ( 30 ,pandesal)} c. {( 10 ,pandesal), ( 20 ,pandesal), ( 30 ,pandesal)} d. {( 10 ,Mamon), ( 20 ,Yema Cake), ( 10 ,Pandesal), ( 30 ,Ensaymada)} 14 - 15. Below are the statements that may represent real life situation using one-to-one function.
14. Which of the following is not included? i. One person has one passport. ii. A shoe has one place on which you would wear it (your foot). iii. Paper has one source. iv. A washing machine has two function (to wash)

a. i only c. iii and iv

b. ii and iii only d. iv only 15 .Which of the following is an example of one-to-one function?

a. i and ii c. iii and iv

b. ii and iv d. i and iv

Lesson

Represent Real-Life

Situation using One-to-One

Functions

Start Lesson 1 0 of this module by assessing your knowledge of representing real-life situation using one-to-one functions. These knowledge and skill will help you understand easily on how to represent real-life situation using one-to-one functions. Seek the assistance of your teacher if you encounter any difficulty.

What’s In

Study the graph below, write the values of y in the table below. Figure 1 Figure 2 x y

• 2
• 1 0 1 2 x y
• 2
• 1 0 1 2

What’s New

Contact five (5) of your classmates to write their Learner’s Reference Number (LRN)

on the table provided below.

Name of the Member Learner’s Reference Number (LRN) Questions:

1. What did you observe from the table? Did you notice any repeated LRN?
2. What do you think is the reason why learners have their own LRNs?
3. What kind of function is depicted from the given activity?

What is It

One-to-One Functions

A function f is one-to-one if it never takes the same value twice or

. That is, the same y-value is never paired with two different x-values. In the Venn diagram below, function f is a one-to-one since not two inputs have a common output.

Figure 1. Venn diagram of a one-to-one function. In the Venn diagram below, function f is NOT a one-to-one since the inputs - 1 and 0 have the same output. Figure 2. Venn diagram of a function that is not a one-to-one. On the other hand, the function g(x) = is not a one-to-one function, because g(−1) = g(1). There are a lot of real-life applications of a one-to-one function. Determine whether the given relation is a function. If it is a function, determine whether it is one-to-one. Example 1: The relation pairing an SSS member to his or her SSS number. Solution: Each SSS member is assigned a unique SSS number. Thus, this relation is a function. Further, two members cannot be assigned the same SSS number, therefore, the function is one-to-one. Example 2: The relation pairing a citizenship to a person. Solution: The relation is a function because each person has a citizenship. However, a person can have two citizenship, (dual citizen) therefore, it is not one-to-one function.

What’s More

Activity 1.1 Understanding One-to-One Functions

Determine whether each of the following situations is a one-to-one function. Elaborate your answer.

1. The relation of a dog to its family members.

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2. The relation of a person to his or her passport.

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3. A car model to its manufacturer company.

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4. A shark to where it lives.

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5. True or False questions to answers.

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Activity 1.2 True or False

Identify whether the following represents one-to-one functions.

1. Degree Fahrenheit to its equivalent degree Celsius measurement
2. Person to his/her citizenship
3. Fare to the distance travelled
4. Cellphone to its cellphone number
5. Length in meters to its length in inches.
6. Father to his first biological son.
7. ATM Card Number to account name
8. Person to his favorite music.

9. House to telephone number.
10. Brand name to pair of shoes.

What I Have Learned

A. Complete the statements below.

1. ________ is a set of ordered pairs in which no two ordered pairs that have the same first component have different second components.
2. When working on the coordinate plane, a function is a one-to-one function when it will pass the _____________ (to make it a function ) and also a ___________ (to make it one-to-one ).
3. Is the Function f : (m,3), (a,2), (t,9), (h,4) represents one-to-one functions? If yes, why? ___________________
4. In the diagram below, set A is the _______ of the function and set B is the _______ of the function. .
5. In a one-to-one function, given any y value, there is only one x that can be paired with the given y. Such functions are also referred to as __________._ B. Which of the following graph shows one-to-one function? State the reason below. Graph A

What I Can Do

Now that you have deeper understanding of the topic, you are ready to solve the problems below. Let the students bring several round containers or lids and record the diameter and circumference in a table. If diameter is the input and circumference is the output, what's the function rule? As they divide each container's circumference by its diameter to find that rule, they should notice a constant ratio -- a rough approximation of pi.

Assessment

Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.

1. It is a rule that produces a correspondence between the elements of two sets: D (domain) and R (range), such that to each element in D there corresponds one and only one element in R. a. Function c. Set b. Relation d. Subset
2. A graph of a function can also be used to determine whether a function is one-to- one using the _____________. a. vertical line test c. t-test b. horizontal line test d. z-test

3. A method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once. a. vertical line test c. t-test b. horizontal line test d. z-test
4. Which of the following is not a one-to-one function? a. c. b. d.
5. Which type of relation wherein every element in the domain is paired with exactly one element in the range? a. Function c. Inverse b. Asymptote d. Composite
6. Which of the following relationships DOES NOT indicate a one-to-one function? a. A tricycle and its plate number c. Parents and their children b. Chemical symbol to its chemical element d. Husband and Wife
7. Which of the following represents a one-to-one function? a. Teacher to students c. Mother to her children b. Student to their LRN d. Students to teacher
8. Consider the graph below. Which of the following line test crosses the graph of a function at no more than one point? Line Test X Line Test Y

a. Line Test X only c. Both Line Test X and Y

b. Line Test Y only d. None of the following.

13. The coffee shop menu, shown in figure below consists of items and their prices. Is the menu represent one-to-one function? MENU Dunkin Donut ₱ 25. Krispy Kreme ₱ 45. Mister Donut ₱ 25.

a. Yes, because each item on the menu has only one price, so the price

is a function of the item.

b. Yes, because one item on the menu has only one price, so the price is a function of the item. c. No, because the two items on the menu have the same price. d. No, because one item on the menu have the same price.

14. The table shows the lists of five greatest volleyball players of all time in order of rank. Is the rank a function of the player name? Is the player name a one- to-one function of the rank? Player Rank Tokyo 1 Nairobi 2 Alicia 3 Lisbion 4 Manila 5 a. Yes c. Maybe b. No d. I don’t know.
15. Is the area of a circle a function of its radius? Which of the following statement proves that the area of a circle a function of its radius.

a. A circle of radius r has a unique area measure given by A= 𝜋r^2 , so for

any input r, there is only one output, A.

b. If the function is one-to-one, the output value, the area, must correspond to a unique input value, the radius. c. Any area measure A is given by the formula A=𝜋r^2. Because areas and radii are positive numbers, there is exactly one solution:√ 𝐴 𝜋

d. All of the choices.

Additional Activities

Below are words which can be associated with one-to-one functions. Write a statement below that may prove it is an example of one-to-one function. Example: Passport ID Answer: A person has only one passport ID.

1. Citizenship
2. Fare
3. Car
4. Area of a circle.
5. Soap