CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Functions

Let’s warm up :

Evaluate the following equations:1) a + 4 = 9

2) b - 4 = 9

3) 4 x c = 16

Write the equations and then solve it.

4) Five times a number is 15.

5) A number divided by 6 is 8.

CONFIDENTIAL 2

Let’s first review what we learnt in the previous sessions before proceeding further.

We learnt about the following term:

We know that variable is a letter that represents a number.

Equation: It is a mathematical statement that has an expression on

the left side of the equals sign (=) with the same value as the

expression on the right side.

The examples of an equation is:

5 + x = 12

2t - 29 = 7

CONFIDENTIAL 3

Review

The equality of two expressions gives an equation.

If two expressions are not equal, an inequality is created.

The inequality symbols used at this grade level are ≠ (is not equal to), > (is greater than), and < (is less

than).

It may also be stated that an equation is ‘two expressions set equal to each

other’.

Solution A value, such that, when you replace the variable with it, it makes

the equation true. (the left side comes out equal to the right side)

CONFIDENTIAL 4

Solve: n + 5 = 9

WAY 1:

WAY 2:

There are different ways of to solve a problem.

Use an addition fact.

n + 5 = 9

n = 4

n + 5 = 9

n + 5 -5 = 9 – 5

n = 4

Use the Inverse Operations.

Subtract 5 from each side.

Think:4 + 5 = 9

So ‘n’ must be

4.

Review

CONFIDENTIAL 5

Review

Solve: 3m = 18

WAY 1:

WAY 2:

Use a related multiplication fact.

3m = 18

m = 6

3m = 18

3 x m ÷ 3 = 18 ÷ 3

m = 6

Use the Inverse Operations.

Divide each

side by 3.

Think:3 x 6 =

18So ‘m’

must be 6.

CONFIDENTIAL 6

Review

We need to use the Inverse Operations to find the value of the variable in the equations.

If the problem has Addition, use Subtraction to solve.

a + 4 = 7a + 4 - 4 = 7 - 4

a = 3

If the problem has subtraction , use Addition to solve.

b - 4 = 5b - 4 + 4 = 5 + 4

b = 9

If the problem has Multiplication ,

use Division to solve.

5c = 155c ÷ 5 = 15 ÷ 5

c = 3

If the problem has Division , use Multiplication to solve.

d ÷ 4 = 4d ÷ 4 x 4 = 4 x4

d = 16

Remember to Use Inverse Operations

CONFIDENTIAL 7

ReviewThe sum of twice a number and 13 is 75. Find the

number.

STEP1: Let the number be denoted by “n”.

So, the equation will be as follows:

2n + 13 = 75

STEP2: Solve the equation.

2n + 13 = 75

2n + 13 - 13 = 75 -13

2n = 622 2

n = 31

Divide both sides

by 2.

Subtract 13 from

both sides.

Hence, the number is 31.

CONFIDENTIAL 8

Let’s start with Functions

First let us know the meaning of the term Function.

FUNCTION : It is a relationship in which one quantity depends upon another quantity.

In other words, Functions are rules that describe the relationship between two variables.

Common examples of functional relationships include the relationship between the unit cost of an item and the cost for multiple numbers of that

item.

For example, y = x + 4.

CONFIDENTIAL 9

Functions are commonly expressed as equations.

When you know the value of one variable, you can use a rule or an equation to find the value of the other variable.

For example, in the function y = 2x + 6, if you know that x = 3, you can calculate that the value of y is 12.

It is important for you to understand that for each value of a variable, there is exactly one related value for the other variable. In the example y = 2x + 6, when x = 3, y can only

equal 12.

CONFIDENTIAL 10

The two variables in a function have names that explain how they relate to one another.

One variable, usually x, is known as the input or independent variable. This is the variable upon which the operation or operations are performed.

The other variable, usually y, is called the output or dependent variable. The value of this variable is dependent upon the value of the independent variable.

CONFIDENTIAL 11

Functions are also displayed or described in the form of function tables or graphs.

A Function Table is a table of ordered pairs that follow the rule for that function.

Function tables can be made up of an infinite number of ordered pairs. A Function Table for the equation y = 2x + 6 is shown

below.

ORDERED PAIR : Two numbers that give the location of a point on a graph or map are called the Ordered Pair.

x 1 2 3 4

y 8 10 12 14

independent variable

dependent variable

Rule y = 2x + 6

CONFIDENTIAL 12

Solve the problem with the help of a function table. Then write the

equation.

One number is 2 more than 3 times another number.

You can write the equation with the help of the given statement.

We are given thatOne number is 2 more than 3 times another

number.

Let the smaller number be ‘x’ and, greater number be ‘y’.

Then the equation will be:y = 3x + 2

We will now solve the problem with the help of Function Table.

STEP1:

CONFIDENTIAL 13

STEP2:We find the values of ‘y’ by

putting the values of ‘x’ in the equation.

When x = 1, y = 3 x 1 + 2, y = 3 + 2 = 5

When x = 2, y = 3 x 2 + 2, y = 6 + 2 = 8

When x = 3, y = 3 x 3 + 2, y = 9 + 2 = 11

When x = 4, y = 3 x 4 + 2, y = 12 + 2 = 14

CONFIDENTIAL 14

Input (x) 1 2 3 4

Output (Y)

5 8 11 14

Rule y = 3x + 2

STEP3:We now make the function table’ by putting the values of ‘x’ and

‘y’ .

CONFIDENTIAL 15

BREAK

CONFIDENTIAL 16

GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/02-27-07-bearshamrocks.html

CONFIDENTIAL 17

Assignments

Complete the function tables according to the given rules:

Question

number

Rule: y = 2x

Input (x) Output (y)

1) 5

2) 18

3) 3

4) 16

CONFIDENTIAL 18

Write the equation:

5) Thrice of a number is 6 more than another number.

CONFIDENTIAL 19

Question

number

Rule: y = 3x - 4

Input (x) Output (y)

6) 2

7) 8

8) 3

9) 11

Complete the function tables according to the given rules:

CONFIDENTIAL 20

Write the equations and then solve it:

10) The number of boys in a class is 4 less than the number of girls. If there are 25 girls in the class, find

what is the number of boys in the class?

CONFIDENTIAL 21

Very Good!Let's Review

FUNCTION : It is a relationship in which one quantity depends upon another quantity.

In other words, Functions are rules that describe the relationship between two variables.

For example, y = x + 4.

The two variables in a function have names that explain how they relate to one another.

One variable, usually x, is known as the input or independent variable. This is the variable upon which the operation or operations are performed.

The other variable, usually y, is called the output or dependent variable. The value of this variable is dependent upon the value of the independent variable.

CONFIDENTIAL 22

Functions are also displayed or described in the form of function tables or graphs.

A Function Table is a table of ordered pairs that follow the rule for that function.

Function tables can be made up of an infinite number of ordered pairs. A Function Table for the equation y = 2x + 6 is shown

below.

ORDERED PAIR : Two numbers that give the location of a point on a graph or map are called the Ordered Pair.

x 1 2 3 4

y 8 10 12 14

independent variable

dependent variable

Rule y = 2x + 6

CONFIDENTIAL 23

Solve the problem with the help of a function table. Then write the

equation.

One number is 2 more than 3 times another number.

You can write the equation with the help of the given statement.

We are given thatOne number is 2 more than 3 times another

number.

Let the smaller number be ‘x’ and, greater number be ‘y’.

Then the equation will be:y = 3x + 2

We will now solve the problem with the help of Function Table.

STEP1:

CONFIDENTIAL 24

STEP2:We find the values of ‘y’ by

putting the values of ‘x’ in the equation.

When x = 1, y = 3 x 1 + 2,

y = 3 + 2 = 5

When x = 2, y = 3 x 2 + 2, y = 6 + 2 = 8

When x = 3, y = 3 x 3 + 2,

y = 9 + 2 = 11

When x = 4, y = 3 x 4 + 2, y = 12 + 2 =

14

Input (x) 1 2 3 4

Output (Y)

5 8 11 14

Rule y = 3x + 2

STEP3:We now make the function table’ by putting the values of ‘x’ and

‘y’ .

CONFIDENTIAL 25

You have done a nice job.See you in the next session.