Question

How do you determine the amplitude, period, and shifts to graph `f(x)= -1.5sin [x+ (pi/4)] +4`?

Answer 1

Amplitude is 1.5 and period is `2pi`.

Explanation:

f(x) is periodic with period P, if f(t+P) = f(t), P > 0 and is the least possible value. The amplitude is half the width for the periodic oscillation of f(x), over a mean value.

So, for f(x) = a sin (bx+c) +d, the amplitude, P = (2pi)/b and the oscillation is between d-a and d+a. So, a is the amplitude.

Here the oscillation is between 4 + 1.5 and 4 - 1.5. So, the amplitude is 1.5, and the period is (2pi)..