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

Sep 2, 2017

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

#### Explanation:

If we consider $A \sin \left[B \left(x + C\right)\right]$, 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. $3 \sin \left(1 \left(x - 1\right)\right)$ 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 $\frac{1}{B} \times 2 \Pi$

So in your case B = 2, so $\frac{1}{2} \times 2 \Pi = \Pi$ radians. This gives us the new period for your graph, this means a complete cycle occurs every $\Pi$ rads instead of every $2 \Pi$ rads.

Then graphing this: $3 \sin \left(2 \left(x - 1\right)\right)$

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