Determine the amplitude and period of the following function without graphing.
y = 8sin(πx)
show your work
The general form of a sine function is y = A*sin(Bx + C) + D, where A is the amplitude and B determines the period. We can rewrite the given function in this form:
y = 8sin(πx)
y = 8sin(πx + 0) + 0
Comparing this to the general form, we can see that:
Amplitude (A) = 8
Period = 2π/B
In the given function, B is π, so:
Period = 2π/π
Period = 2
Therefore, the amplitude of the function is 8 and the period is 2.