Question

How do you sketch `y = 3 sin 2 (x-1)`?

Answer 1

graph{3sin(2(x-1)) [-10, 10, -5, 5]}

Explanation:

If we consider `Asin[B(x+C)]`, the first term A is increasing the amplitude of the sin graph. So if we make A = 3 we would get the following graph.

graph{3sinx [-10, 10, -5, 5]}

We will look at C next, this is the movement of the graph left or right, where a negative C value moves the graph to the right. So we move the whole graph 1 to the right in this case. `3sin(1(x-1))` give the following graph.

graph{3sin(x-1) [-10, 10, -5, 5]}

Finally B is stretching the graph parallel to the x axis by a factor of `1/B xx 2Pi`

So in your case B = 2, so `1/2 xx 2Pi = Pi` radians. This gives us the new period for your graph, this means a complete cycle occurs every `Pi` rads instead of every `2Pi` rads.

Then graphing this: `3sin(2(x-1))`

graph{3sin(2(x-1)) [-10, 10, -5, 5]}