### Video Transcript

The figure shows the graph of π¦ equals π of π₯ and point π΄, which is a local maximum. Identify the corresponding local maximum for the transformation π¦ equals π of π₯ minus three.

We need to recall firstly our rules for transformations and what π of π₯ minus three represents. We should recall that π of π₯ minus π for some constant π is a translation π units in the positive π₯-direction. The graph of π of π₯ minus π will be the graph of π of π₯ but simply shifted or moved π units to the right. In this specific example, weβve been given the value of π is three. So weβre looking at a translation three units in the positive π₯-direction. Weβre also asked specifically to identify where the point π΄, which is a local maximum on the original graph, is translated to.

Well, if we are translating the graph three units to the right, then the π₯-coordinate will increase by three, but the π¦-coordinate will be unaffected. The new π₯-value will therefore be two plus three, and the new π¦-value will be the same as it was before. The point two, one is therefore translated to become the point five, one. So we found that if π΄ is the local maximum for the graph π¦ equals π of π₯, then the corresponding local maximum for the transformation π¦ equals π of π₯ minus three is the point five, one.