Video Transcript
The figure shows the graph of 𝑓 of
𝑥. A transformation maps 𝑓 of 𝑥 to
𝑓 of 𝑥 minus two. Determine the coordinates of 𝐴
following this transformation.
We begin by recognizing the red
curve as the graph of the main cosine function. The features that clued us into
this fact are the amplitude of one, the period of 360, the 𝑦-intercept at one, and
the 𝑥-intercepts at 90 and 270. For this example, we need to
identify the effect of the transformation that maps 𝑓 of 𝑥 onto 𝑓 of 𝑥 minus
two. In particular, we will calculate
the effect on the coordinate point 180, negative one. The coordinates of point 𝐴
correspond to the fact that cos of 180 degrees equals negative one. So, we can find the new coordinate
by finding the value of 𝑓 of 𝑥 minus two at 𝑥 equals 180. That is cos of 180 minus two. And we know that cos of 180 equals
negative one. So, 𝑓 of 180 minus two equals
negative three. Therefore, the given transformation
maps 180, negative one to 180, negative three.
