In this section you will be given a function that has already been graphed and you will be able to write the equation (f(x)=AsinB(x-h)+k or f(x)=AcosB(x-h)+k). When looking at a graph there are specific questions you should ask yourself (located below). You will be using your knowledge from the previous section.

Questions to Ask Yourself?
1. What is the axis of wave? Has the graph been shifted vertically or horizontally?
2. What is the amplitude?
3. What is the period? How does the period effect the equation of a function and vice versa?
4. Which function is represented in the graph? The decision you make here impact the use of horizontal shifts.

Reminder:
Amplitude: the absolute value of the distance from the axis of wave to the maximum or minimum. It can also be found by dividing the distance between the maximum and the minimum by two.
Axis of wave: represents any vertical shift
Period: distance it takes to go through one cycle. It can be determined by finding the distance between a maximum to a maximum, a minimum to a minimum or the distance between three intercepts. The period can be used to determine B, which is equal to: 2pi/P.

Example Problems:

2. A sine function with a period of 8pi and an amplitude of 3. The function is not reflected.

3. A reflected cosine function has a maximum value of 7 and has not been shifted. The horizontal distance between the consecutive x-intercepts is 9pi.

4. The distance between two consecutive minima is 4 units. The graph has a maximum at x=0, and the amplitude is 15.

5. A cosine function has a maximum value of 10 and a minimum value of 4. The quarter-period is 6 units. The function starts at a maximum on the y-axis.

Textbook:PWL 4.5 & 4.6

AM 8.2 & 8.3

Websites:Practice

Practice & Examples (click puzzles and problems)

Questions to Ask Yourself?1. What is the axis of wave? Has the graph been shifted vertically or horizontally?

2. What is the amplitude?

3. What is the period? How does the period effect the equation of a function and vice versa?

4. Which function is represented in the graph? The decision you make here impact the use of horizontal shifts.

Reminder:Amplitude: the absolute value of the distance from the axis of wave to the maximum or minimum. It can also be found by dividing the distance between the maximum and the minimum by two.

Axis of wave: represents any vertical shift

Period: distance it takes to go through one cycle. It can be determined by finding the distance between a maximum to a maximum, a minimum to a minimum or the distance between three intercepts. The period can be used to determine B, which is equal to: 2pi/P.

Example Problems:2. A sine function with a period of 8pi and an amplitude of 3. The function is not reflected.

3. A reflected cosine function has a maximum value of 7 and has not been shifted. The horizontal distance between the consecutive x-intercepts is 9pi.

4. The distance between two consecutive minima is 4 units. The graph has a maximum at x=0, and the amplitude is 15.

5. A cosine function has a maximum value of 10 and a minimum value of 4. The quarter-period is 6 units. The function starts at a maximum on the y-axis.