Question

What is the period of the graph of y= 1/2 sin(pi x) + 3?

A. Pi
B. 2
C. 3
D. 1/2

Answer 1

Explanation:

The period is 2.

Normally the period of sin(x) is 2pi, but the pi inside the sin(pix) is a horizontal compression by a factor of 1/pi. So 2pi·1/pi = 2

The "1/2" and "+3" do not impact the period. Those just impact the amplitude (vertical aspect) of the graph.

Answer 2

B. 2

Explanation:

The standard form of a sine function is given by:

y = A sin(Bx - C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In the given function y = 1/2 sin(pi x) + 3, we can see that the amplitude is 1/2, the frequency is pi, the phase shift is 0, and the vertical shift is 3.

The period of a sine function is given by:

Period = 2π/B

In this case, B = pi, so the period is:

Period = 2π/pi = 2

Therefore, the period of the graph of y = 1/2 sin(pi x) + 3 is 2, which is option B.