Question

Graph of y = sec x and y = 3sec(2x) are shown. Identify each graph, explaining your reasoning. http://gyazo.com/681d55dabc85cb379b6425750181d1f6

I know that the red graph is 3sec(2x) and the blue is sec(x) I just don't know how to explain it...

Answer 1

Would this be an acceptable reason: I knew that the red graph was 3sec(2x) simply by looking at the 3 and notcing that the red graph starts at 3. I just need help turning that into trig terms...

Answer 2

@cwrw238

Answer 3

sec x can be written as 1/cos(x)

what is cos(0) ? it is 1. when x is 0, 1/cos(x) is 1
in other words (0,1) is a point on the graph of sec x

what about 3 sec x ? at x =0 , 3*sec(0) = 3... (0,3) is on the graph of 3 sec(2x)

so one reason the red graph is 3 sec(x) is because you know (0,3) is a point on its graph, and only the red graph goes through (0,3).

Answer 4

you should also know that when you have sec(x) and sec(2x)
the "2" makes the sec(2x) "skinnier" than sec(x).

you can see the red graph is skinner than the blue graph, so the red graph must be the one that uses sec(2x)... in other words, it must be 3 sec(2x) rather than the other equation sec(x)

Answer 5

It makes it "skinnier" because it repeats itself more often correct?

Answer 6

I think I understand what you are saying... but maybe say it repeats more often in a fixed interval... (both graphs repeat forever, so it does not sound right to say one repeats more often than the other)

Answer 7

Okay, I think I'll just leave that out. I only need one supporting detail for my answer. Thank you very much phi!