Question

identify the amplitude, vertical shift and period of this function y=-3 cos(2x)+1
also, how do i graph at least two periods of the function?

Answer 1

amplitude= -3? and vertical shift 1 up?

Answer 2

Remember amplitude is \[\left| A \right|\] so A is going to be positive 3. The vertical shift is 1 up. That is correct. The period remember is \[T=\frac{ 2\pi }{ \omega}\]

Finding the period helps us to graph the function by taking the period and dividing it up into 4 equal intervals.

Answer 3

So, in this case, your period is going to be \[T=\frac{ 2\pi }{ 2 }=\pi \] So, divide your period by 4, and you get the intervals to graph your function. The first interval goes from 0 to pi/4. The second interval goes from pi/4 to 2pi/4. The third interval goes from 2pi/4 to 3pi/4, and the last interval goes from 3pi/4 to 4pi/4.

Answer 4

Note that this is only 1 period. You have to graph 2 periods, so just continue adding pi/4 to each interval until you get 8pi/4 which would complete the 2 periods required.

Answer 5

but the graph i have with me it pi/2, pi, 3pi/2 and 2pi for the x axis and up to 4 for the y axis

Answer 6

Fine. Just take each interval and cut them in half. So half way between 0 and pi/2 is pi/4.