1. 2.4 - 2.5 Families of Functions, Piecewise, and Transformations

4. Piecewise functions consist of different function rules for different parts of the domain.

5. 2x + 1 if x ≤ 2 x 2 – 4 if x > 2 h(x) = h(–1) = 2(–1) + 1 = –1 h(4) = 4 2 – 4 = 12 Evaluate each piecewise function for x = –1 and x = 4. To evaluate any piecewise function for a specific input, find the interval of the domain that contains that input and then use the rule for that interval.

6. 2 x if x ≤ –1 5x if x > –1 g(x) = g(4) = 5(4) = 20 g(–1) = 2 (–1) = 1 2 Evaluate each piecewise function for x = –1 and x = 4.

7. 3x 2 + 1 if x < 0 5x – 2 if x ≥ 0 g(x) = g(3) = 5(3) – 2 = 13 g(–1) = 3(–1) 2 + 1 = 4 Evaluate each piecewise function for x = –1 and x = 3.

8. g(x) = 1 4 Graph each function. x + 3 if x < 0 –2x + 3 if x ≥ 0

14. The rounding down function is also called the greatest integer function.

15. Greatest integer or rounding down function

19. Example: Describe the transformations that have taken place in each of the related graphs: