Question

Which function's graph has a period of 2?

Answer 1

Answer:

Option 2. y = 3 cos πx is the answer.

Step-by-step explanation:

If the function is in the standard form of y = acos(bx+c)  or y = asin(bx+c)

Then period of the given function will be = 2π/b

1) For y = cos(x - π/2)

Therefore period of the function will be = 2π/1 = 2π

2) For y = 3cos πx

Period = 2π/π = 2

Correct option.

3) y = 2 sin 3x

Period of the function = 2π/3

4). y = -4sin 2x

Period of the function = 2π/2 = π

So option 2 is the answer.

Answer 2

If the function is:
y=a cos( bx+c), or y=a sin(x+c)
then the period is T= 2π/b and if T=2:
2=2π/b
b=2π/2=π
Answer: B) y=3 cos πx