Graph a Secant Function (sec) Using Amplitude and Period

In this video we graph y = 3 sec (-4x) using the graph of y = 3cos(-4x). Amplitude, period, and the fact that cosine and secant are even functions are also covered.

[boring-username]

You touched on the one aspect of the secant graph that almost every videos fails to mention; you cannot take the reciprocal of the cosine function when the graph is vertically stretched or shrunk. This also holds true for the graphs of cosecant.

The way most videos introduce the secant/cosecant graphs can set you up for confusion. First, they'll introduce the parent cosine or sine graphs, e.g., y = cos(x), and explain how you can take the reciprocal at every point to determine the points for their respective reciprocal graphs, e.g., y = sec(x).

However, while that's technically correct, they fail to ever mention that this technique will not work once you have applied a vertical stretch or shrink to the parent function, .e.g, y = 3cos(x) for reasons like you described in this video. To make things even more confusion, they'll still graph the vertical asymptotes of those transformed functions by explaining the reciprocal technique, but then conveniently ignore it for the local minimum and maximum points of the transformed function.

Thank you so much for explaining this caveat and not relying entirely on the memorization techniques that other videos seem to leverage.