1. Section 2.1.2 Shifting Functions & Periodicity

2. OBJECTIVES SWBAT: SWBAT explain the effect of shifts for piecewise functions. Shift functions (including piecewise functions) both vertically and horizontally and recognize periodic functions.

4. 2-15 a: It is shifted to the left two units.

6. 2-16 g(x) should be shifted to the right one and up 3.

8. 2-17 c: At x = 3. a: b:

10. 2-18 a: Shifts left 2 and down 3. C:

11. A function whose graph repeats itself identically, over and over, as it is followed from left to right. Periodic Function

13. 2-19 c: No asymptotes, but translational symmetry is present. Any multiple of 5 will work; 5n where n is any integer. d: The function is made up of line segments but it does not belong to any previously studied family. a: D : all Real Numbers R : [2, 4] b: (0, 2)

14. Periodic functions have “periodicity,” which simply means that they repeat at regular intervals. Ex: Clocks, metronomes, and periodicals To describe the periodicity of a function, it is the period with the smallest shift possible that preserves the function’s appearance.

16. 2-20 a: Yes, the difference in the x-values, 17 – 2 = 15 which is a multiple of the period, 5. b: Yes, shifting the function horizontally by its period will result in a graph that is identical to the original. c: 8 solutions

18. 2-21 a: p = 7 b: The values visible on the graph are ≈ -2.5, 0.5, 4.5, and 7.5. b: Find two more solutions using the idea that -2.5 + 7n and -0.5 + 7n in which n is an integer are also solutions. c: g(4) = 2 c: g(53) = g(4 + 49) = g(4 + 7p)

19. Assignment Pg 70 #2-22 TO 2-30