### Video Transcript

The figure shows the graph of π of π₯. A transformation maps π of π₯ to two π of π₯. Determine the coordinates of π΄ following this transformation.

And then we have a graph, which gives us coordinates of π΄ as 90, one. So to answer this question, letβs begin by thinking about the algebraic representation of transformations. Specifically, which transformation maps π of π₯ to two π of π₯? Well, suppose we have the function π of π₯. This is mapped onto ππ of π₯ by a vertical stretch, scale factor π. This means we can map π of π₯ onto two π of π₯ by a vertical stretch with a scale factor of two. And whilst the axes donβt quite go up far enough, we can sketch this approximately on our diagram. A vertical stretch by a scale factor of two will maintain the same π₯-intercepts.

For all other coordinates, the π¦-values will essentially be doubled. And so if we were to draw the graph of π¦ equals two π of π₯, it might look a little something like this. Letβs then say that point π΄ is mapped onto point π΄ prime following this transformation. What are the coordinates of point π΄ prime? Well, we said actually the π₯-coordinates stay the same, and what happens is the π¦-coordinates are all multiplied by two. So π΄ prime must have coordinates 90, one times two, which is 90, two.

Now, in fact, if we think about the equation of each graph, this makes a lot of sense. Notice that our original graph is sinusoidal. It has maxima and minima of one and negative one, respectively, and a π¦-intercept of zero. It also appears to repeat; itβs periodic with a period of 360 degrees. In fact, the function π of π₯ is sin of π₯. This means that two π of π₯ must simply be two sin of π₯.

So after the transformation, we have to plot the graph π¦ equals two sin of π₯. We might do that using a table or any other suitable method. Either way, we should observe that point π΄ maps onto point π΄ prime with coordinates 90, two. The coordinates of π΄ following our transformation then are 90, two.