1. 2.5 Warm Up Graph, identify intercepts, zeros, and intervals of increase and decrease. Compare to parent function. y = 2 x + 3 - 1

2. 2.5 Using Piecewise Functions

3. Vocabulary Piecewise function: –Has at least 2 equations –Each has a different part of the domain Points of Discontinuity: –Point where there is a break in the graph Step Function –Piecewise function that is continuous –Looks like stairs Extrema: –Max/Min of function –Local (within given domain) or Global (within entire domain) Average rate of change: –Slope

4. Evaluate the function when x = 5 and x = -2 g(5) = 2(5)+1 Since 5 is greater than 0, use 2x+1 g(5)=11 g(-2) = 3(-2) -1 Since -2 is less than 0, you use 3x-1 g(-2) = -7

5. 1.f(-6) 2.f(2) 3.f(3) 4.f(4)

6. Graph the 1 st equation stopping at its extrema When x is 0, you should have a solid point Line should be to the left since it is less than Graph the 2 nd equation stopping at its extrema When x is 0, you should have an open circle Line should be to the right since it is greater than Points of discontinuity? To Graph

7. Graph

8. Let’s look at p. 50 #5

9. To write a piecewise function Graph the function if not already graphed Break it into parts Identify the domain for each part Write an equation for each part

10. Write a piecewise function for f(x) = 2│x+4 │-12 Vertex = (-4,-12) x<-4 y = 2x-4y = -2x-20

11. What is the extrema and rate of change of f(x) = 2│x+4 │-12? Since the vertex is (-4, -12), the minimum (extrema) is -12. When x>-4, the rate of change is 2. When x<-4, the rate of change is -2.

12. The greatest integer function (or floor function) will round any number down to the nearest integer. The notation for the greatest integer function is [#] or #. A ceiling function will round any number up to the nearest integer. # Step Function: