Function Composition: Graphing f(g(x)) Without Equations

[SD-Ness]

Hello, I've been an intermittent poster here for about five years. I've come back for another shot at PF. So for a first thread:

Class is a currently a review of old topics. One of them is 'function composition.' I was doing an assignment today and came upon a question that required one to graph f(g(x)) from two graphs given f(x) and g(x). There were no equations supplied. How might one go about graphing f(g(x))? I am not sure of the relationship here, unfortunately.

 

[Dorothy Weglend]

Class is a currently a review of old topics. One of them is 'function composition.' I was doing an assignment today and came upon a question that required one to graph f(g(x)) from two graphs given f(x) and g(x). There were no equations supplied. How might one go about graphing f(g(x))? I am not sure of the relationship here, unfortunately.

It sounds like you have two graphs, and have to generate a third one, f(g(x)) from the graphs of f(x) and g(x)?

Well, right now, you have y=g(x) and y=f(x). But you want a graph which is y=f(g(x)). Is this enough to get you started? This sounds like a pain, BTW.

Dot

 

[SD-Ness]

It sounds like you have two graphs, and have to generate a third one, f(g(x)) from the graphs of f(x) and g(x)?

Well, right now, you have y=g(x) and y=f(x). But you want a graph which is y=f(g(x)). Is this enough to get you started? This sounds like a pain, BTW.

Dot

Yes, this is correct. I have two graphs - f(x) and g(x) - and I need to generate the third, f(g(x)).

I know that y=g(x) and y=f(x), but I'm not sure how to generate y=f(g(x)) from that.

 

[alias25]

let x=g(x), to sub into the equation y = f(x)? don't know if its an help. its a strange question.

 

[Dorothy Weglend]

Yes, this is correct. I have two graphs - f(x) and g(x) - and I need to generate the third, f(g(x)).

I know that y=g(x) and y=f(x), but I'm not sure how to generate y=f(g(x)) from that.

The only difference is that you have to look up the values on the graphs, instead of compute them. A = g(x), y = f(A), this is how you would compute a function composition, right? These X's and Y's would be the coord's of the point on the new graph. The intermediate value of A is just used to look up the proper value of the function composition.

I'm assuming here that the graphs are complicated, and it's not possible to recover the functions that generated them. If they are simple, like a straight line or a parabola, then you could recover the functions (or make a good guess) and generate a formula to plot the new graph directly.

Dot

Dot