Composition of Trig Functions

[harpazo]

Given f(x) = csc x, A(x) = | x | and g(x) = sec x, graph the indicated functions over the interval [-2pi, 2pi].

1. A (g(x))

2. f(A(x))

Question 1

I believe the set up is A(g(x)) = | sec x |.
Now, just graph the absolute value of sec x.
Yes?

Question 2

The set up is f(A(x)) = csc (| x | ). Now just graph cosecant of the absolute value of x.
Yes?

 

[pka]

Given f(x) = csc x, A(x) = | x | and g(x) = sec x, graph the indicated functions over the interval [-2pi, 2pi].
1. A (g(x))
2. f(A(x))
Question 1
I believe the set up is A(g(x)) = | sec x |.
Now, just graph the absolute value of sec x.
Yes? CORRECT
Question 2
The set up is f(A(x)) = csc (| x | ). Now just graph cosecant of the absolute value of x.
Yes? CORRECT

Good

 

[harpazo]

Good

Cool. I finally understood something on my own. I will post the graph for 1 and 2.

 

[harpazo]

Good

Graph of A(g(x))



Graph of f(A(x))

 

[Dr.Peterson]

Those are good. Could you have sketched them by hand, or at least seen how the graphs of sec(x) and csc(x) have to be modified to obtain them? Absolute values in graphing can confuse some students.

 

[harpazo]

Those are good. Could you have sketched them by hand, or at least seen how the graphs of sec(x) and csc(x) have to be modified to obtain them? Absolute values in graphing can confuse some students.

I am currently learning how to graph tangent, cotangent, cosecant and secant by hand watching You Tube clips. To answer your question, not at this time. I expect to have a better grasp of graphing the above functions by Sunday.

 

[Steven G]

Graph of A(g(x))

View attachment 19328

Graph of f(A(x))

View attachment 19329

Hi,
You did not graph these functions. Can you?

 

[harpazo]

Hi,
You did not graph these functions. Can you?

Read my reply to Dr. Peterson. My main focus here was to make sure I understood the set up for the two composition of trig functions.

 

[Steven G]

I am currently learning how to graph tangent, cotangent, cosecant and secant by hand watching You Tube clips. To answer your question, not at this time. I expect to have a better grasp of graphing the above functions by Sunday.

Watch the video from here, here and here

 

[harpazo]

Watch the video from here, here and here

Thanks but I have a selected tutor on You Tube for this purpose. I will not be able to do this today. Be back in a moment.

 

[harpazo]

Watch the video from here, here and here