Question

21 points!!

For questions 6 – 8, complete the following for the function:
(a) Sketch two complete cycles of the graph.
(b) What is the period?
(c) What is the amplitude?
(d) How is this graph related to its parent graph or ?

6.) y= 5sin2x


7.) y= 3cos(x/2)

8.) y= 2sin(2πx)+1

Answer 1

See attached pictures.

Explanation:

The sine and cosine functions have the forms:
`f(x) = C+ A sinBx` and
`f(x) = C + A cosBx`. A is the amplitude for each function. The period is found by dividing 2π the absolute value of B or
`(2\pi)/(|B|)`. C shifts the function up and down.

The sine function always starts and ends on the x-axis.

The cosine function always starts and ends at the y=A.

6.) The sine function starts at (0,0) then peaks at 5. Comes down to 0 and down to -5 before returning to 0.

The amplitude is 5.

The period is
`(2\pi)/(|2|)=\pi`

7.) Here A=3 so the amplitude is 3, B is 1/2 so the period is 4π. Start at (3,0) and descend down to (2π, 0). Go back up to (4π, 3).

8.) Here A = 2 so the amplitude is A. B is 2π so the period is 1. C is 1 so the graph is shifted up a unit.

Start the graph at (0,1) and go up to (0.25,3) and down to (0.5,1) and continue downward to (0.75, -3) then back up to (1,1).