So if you remember what the normal y = sin(x) function looks like (a wave), y = 2 sin(4x) is just changed a little.
The standard format for sine/cosine function <span>y = a sin<span>(bx− c)</span> + <span>d
a = amplitude, distance from center of the wave to the highest point. This function a = 2 so the height of the sine wave reaches 2 instead of 1. "c" and "d" shift the graph left/right and up/down respectively. These equal zero so the sine wave is not shifted.
The range (y-values) is then just the amplitude -2 ≤ y ≤ 2
The domain (x-value) is all real numbers because the wave just keeps going on to infinity in both directions.
2π / |b| = period, distance per wave this equation b = 4 period is then π/2 this is the distance before a wave repeats.
Graph x | y -π/8 -2 0 0 π/8 2 3π/8 -2 5π/8 2
see the pattern? I'm using the amplitude or peaks and bottoms of the wave y = 2 and -2 then using the x-distance between like points is the period so you add π/2
(π/8 , 2) + π/2 (5π/8 , 2)
Same for the minumums of the wave (y = -2) (-π/8 , -2) + π/2 (3π/8 , -2)
Hope this helps, otherwise there are youtube videos you can watch or try an online graphing calculator like Desmos.com
