1. Piecewise Functions 2.7 What is a piecewise function? How are they evaluated, graphed, written, and used? What is a step function? What is a greatest integer function?

2. Piecewise Function Definition Functions represented by a combination of equations, each corresponding to a part of the domain.

3. Evaluating a Piecewise Function Evaluate f(x) when (a) x=0, (b) x=2, and (c) x=4. f(x) = x + 2, if x < 2 2x + 1, if x ≥ 2 (a)f(x) = x+2f(0) = 0+2=2 (b)f(x) = 2x+1f(2) = 2(2)+1=5 (c)f(x) = 2x+1f(3) = 2(3) +1=7

4. Graphing a Piecewise Function 1 0 2 3

5. Graphing a Step Function

6. Step Function The last example was called a step function because its graph resembles a set of stair steps. Another example of a step function is the greatest integer function. This function is denoted by g(x)=[[x]]. For every real number x, g(x) is the greatest integer less than or equal to x. This graph is on page 115 in your book.

7. Write equations for the piecewise function whose graph is shown. Write the equation for the ray to the left of x=0. y=x+2, if x<0 Write the equation of the ray to the right of x=0 y=x, if x≥0 (-2,0) (0,2) (0,0) (2,2)

8. Greatest Integer Function The greatest integer function is an example of a step function that uses integers. This function is denoted by g(x)=[[x]]. For every real number x, g(x) is the greatest integer less than or equal to x. 0 1 2 0, if 0 ≤ x < 1 1, if 1 ≤ x < 2 2, if 2 ≤ x < 3 xy y = x

9. Step Functions A step function is a piecewise function that consists of different constant range values for different intervals of the domain of the function. 1 -2-3 2 -3 -2 3 1 3 2 Rounding-down function 1 -2-3 2 -3 -2 3 1 3 2 Rounding-up function Greatest integer function

10. http://www.icoachmath.com/SiteMap/Greate st_Integer_Function.html http://www.5min.com/Video/Graphing-the- Greatest-Integer-Function-160960905

11. Using a Step and Piecewise Function Turn to page 116 in your book.

12. What is a piecewise function? How are they evaluated, graphed, written, and used? What is a step function? What is a greatest integer function?

13. Assignment 2.7 Page 117,13-29 odd, 35-39,50-51