Greatest Integer/Absolute Value Functions Students will be able to find greatest integers and absolute values and graph the both functions.

Greatest Integer Another special function that we will be studying is the greatest integer function. The greatest integer function of a real number x, represented by [x], is the greatest integer that is less than or equal to x. For example: [4.25] = 4 [6] = 6 [5.99] = 5 [-2.3] = -3 FHS Functions

Determine whether each statement below is true or false for all real numbers x and y. [x] + [y] = [x + y] if x = 4.2 and y = 3.1, then x + y = 7.3 [4.2] + [3.1] = [7.3] 4 + 3 = 7 Is this correct? if x = 4.7 and y = 3.9, then x + y = 8.6 [4.7] + [3.9] = [8.6] 4 + 3 = 8 Is this correct? FHS Functions

Graph The greatest integer function is sometimes called a step function, because of the shape of its graph. Graph y = [x] y x y = [x] FHS Functions

Graph What happens when we change the function? First multiply the function by 2. Graph y =2[x] On calculator: y = 2int(X) y x y = [x] FHS Functions

Graph What happens when we change the function? Next multiply the independent variable by 2. Graph y =[2x] On calculator: y = int(2X) y x y = [x] FHS Functions

Absolute Value All integers are composed of two parts – the size and the direction. For example, +5 is five units in the positive direction; –5 is five units in the negative direction. The absolute value {written like this: }of a number gives the size of the number without the direction. For example, = 5 and = 5. The answer is always positive. FHS Functions

Absolute Value Graphing the absolute value function. Graph: x y -4 -2 2 4 4 2 FHS Functions