Transformations with Trigonometry

(Section 17)

As mentioned early in this review it is important to understand such transformations as f(kx) and f(x+k) on a functions f(x). Study these examples and relate them to the early transformations discussed. Viewing Window for each graph: [-6.15,6.15,1.57,-4,5,1]

1.	Shrinking factor: 2
2.	horizontal shift:
3.	vertical shift: 3, shrinking factor: 3
4.	vertical shift: 2 horizontal shift: shrinking factor: 4 amplitude change factor: 3

**Note the window selected for examples 3 and 4 make the sine and cosine functions appear pointed. This is just a graphing calculator phenomena.**

Check your understanding: (Remember to write down your answers.)

1. Sketch a graph of each of the following on the interval (-2, 2) by thinking about the horizontal shift, vertical shift, amplitude change, and shrinking and stretching factors. Give a justification for each of your changes.

(Section 17)

**Note the window selected for examples 3 and 4 make the sine and cosine functions appear pointed. This is just a graphing calculator phenomena.**

Check your understanding: (Remember to write down your answers.)

1. Sketch a graph of each of the following on the interval (-2, 2) by thinking about the horizontal shift, vertical shift, amplitude change, and shrinking and stretching factors. Give a justification for each of your changes.

a.

b.

c.

d.

e.

f.