CONFIDENTIAL1 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.

CONFIDENTIAL2 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

CONFIDENTIAL3 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)

CONFIDENTIAL4 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 = 9 – 5 n = 4 Use the Inverse Operations. Subtract 5 from each side. Think: = 9 So ‘n’ must be 4. Review

CONFIDENTIAL5 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 = 18 So ‘m’ must be 6.

CONFIDENTIAL6 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 = 7 a = a = 3 If the problem has subtraction, use Addition to solve. b - 4 = 5 b = b = 9 If the problem has Multiplication, use Division to solve. 5c = 15 5c ÷ 5 = 15 ÷ 5 c = 3 If the problem has Division, use Multiplication to solve. d ÷ 4 = 4 d ÷ 4 x 4 = 4 x4 d = 16 Remember to Use Inverse Operations

CONFIDENTIAL7 Review The 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 = n = 622 n = 31 Divide both sides by 2. Subtract 13 from both sides. Hence, the number is 31.

CONFIDENTIAL8 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.

CONFIDENTIAL9 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.

CONFIDENTIAL10  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.

CONFIDENTIAL11  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. x1234 y independent variable dependent variable Rule  y = 2x + 6

CONFIDENTIAL12 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 that One 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:

CONFIDENTIAL13 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 = = 5 When x = 2,y = 3 x 2 + 2, y = = 8 When x = 3,y = 3 x 3 + 2, y = = 11 When x = 4,y = 3 x 4 + 2, y = = 14

CONFIDENTIAL14 Input (x)1234 Output (Y) Rule  y = 3x + 2 STEP3: We now make the function table’ by putting the values of ‘x’ and ‘y’.

CONFIDENTIAL15 BREAK

CONFIDENTIAL16 GAME Click on the link below for some exciting puzzle puzzles/12-piece-jigsaw/ bearshamrocks.html

CONFIDENTIAL17 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

CONFIDENTIAL18 Write the equation: 5) Thrice of a number is 6 more than another number.

CONFIDENTIAL19 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:

CONFIDENTIAL20 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?

CONFIDENTIAL21 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.

CONFIDENTIAL22  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. x1234 y independent variable dependent variable Rule  y = 2x + 6

CONFIDENTIAL23 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 that One 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:

CONFIDENTIAL24 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 = = 5 When x = 2, y = 3 x 2 + 2, y = = 8 When x = 3, y = 3 x 3 + 2, y = = 11 When x = 4, y = 3 x 4 + 2, y = = 14 Input (x)1234 Output (Y) Rule  y = 3x + 2 STEP3: We now make the function table’ by putting the values of ‘x’ and ‘y’.

CONFIDENTIAL25 You have done a nice job. See you in the next session.