Periodic functions

Question

Graph one full period of the following function. State the amplitude, period, midline, maximum, and minimum y-values and their corresponding x-values on one period.

f(x) = 3 sin(πx + π) + 1

Answer 1

Hi Bernadet,

It's easiest to graph sine functions when they're in the form:

f(x) = A sin (B(x-C)) +D

In this form, A is the amplitude. B can be used to find the period. C is the phase shift, and D is the vertical shift.

Yours is close!! If we pull out the GCF pi, you would have:

f(x)= 3 sin (pi (x-1)) +1

MIDLINE: Normally, the midline of sine is y=0. In your graph, you have a vertical shift up 1. Given this, the midline is y=1.

AMPLITUDE: The amplitude is 3.

MAX Y-VAL: This means that from 1, you can go up 3 values to find the maximum.

MIN Y-VAL: Similarly, from 1, you can go down 3 values to find the minimum.

PERIOD: The normal period of a sin graph is 2pi. In order to find the period of this sin graph you can evaluate 2pi/B, which for your graph is 2pi/pi. Your period is 2.

PHASE SHIFT: You also have a horizontal shift 1 unit to the right.

PUTTING IT ALL TOGETHER:

1. label the y-axis in 1 unit increments
2. draw a dashed line at y=1 to represent your midline.
3. label the x-axis in 0.5 unit increments (I find the best way to label an x-axis for a trig graph is to take the period and divide it by 4. This makes the graphing much simpler as you'll see in a second.)
4. sine graphs start at the midline, then go to the maximum point, then the midline, then the minimum point and repeat.
5. put your first point at (1,1). The x-value is 1 because of the phase shift right 1. The y-value is 1 because it's the midline
6. the next point will be (1.5, 4).

Can you continue from here?!