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

1 Answer
Eric C.
Sep 2, 2017

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]}

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