Graphing Greatest Integer Functions

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Presentation transcript:

Graphing Greatest Integer Functions

Step Functions – functions whose graphs resemble sets of stair steps. Greatest Integer Function – the most notable step function Notation of Greatest Integer Function : x Meaning of Greatest Integer Function : the greatest integer less than or equal to x.

2 2 ? 9 9 ? -3 -3 ? = = = Let’s evaluate some greatest integers… the greatest integer less than or equal to x. -3 = -3 ?

2.2 2 ? 1/2 ? -4.1 -5 ? = = = Let’s evaluate some greatest integers… the greatest integer less than or equal to x. 1/2 = ? -4.1 = -5 ? 1 2 3 -1 -2 -3 -4 -5

Let’s evaluate some greatest integers… 9.1 = ? 9 the greatest integer less than or equal to x. 51/3 = 5 ? -22/9 = -3 ? 1 2 3 -1 -2 -3 -4 -5

x y .25 .5 .75 1 1.25 1.5 1.75 2 Now that you know how to evaluate greatest integer functions, you can graph them. y = x

Now that you know how to evaluate greatest integer functions, you can graph them. x y .25 .5 .75 1 1.25 1.5 1.75 2 y = x +2

x y .25 .5 .75 1 1.25 1.5 1.75 2 Now that you know how to evaluate greatest integer functions, you can graph them. y = x - 4

x y .25 .5 .75 1 1.25 1.5 1.75 2 Now that you know how to evaluate greatest integer functions, you can graph them. y = -x + 2