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[SD-Ness]

So calculus 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.

In other words, in case that was confusing...

f(x) was graphed in a coordinate plane.
g(x) was graphed in a coordinate plane.

And the question asked me to graph f(g(x)) from that.

 

[Ecrofirt]

You'd have to do something like this:

f(x) = 2x + 3
g(x) = -3x - 12

f(g(x)) = 2(-3x - 12) + 3
f(g(x)) = -6x - 24 + 3
f(g(x)) = -6x - 21


Since they're graphec on a coordinate plane, you'll have to figure out what f(x) and g(x) are.

 

[SD-Ness]

Yeah, if it was that simple I'd be fine.

The equations of the graphs are much more complex. But I guess I'll have to take the hard route.

Is there any way to do it graphically though?

 

[Bizarro Sun Yat-sen]

There's no elegant general way to do it graphically, but you can plot a lot of points and try to intuit a curve.

By the way, if you're at all interested in function combinators, take some time to learn about the lambda calculus which is fascinating and has extensive applications in computer science.

 

[slayn]

just draw an empty graph and start from 0, 1, 2 etc and connect via whatever curve looks appropriate.

That is, start with 0. Look at the value at zero on the f(x) graph. take that value and move to the g(x) graph and look at the y value at that x coordinate. Then plot that point at 0 on your new graph.

do for enough points until you can draw a curve that kinda fits them.

and I think lambda calculus is a *bit* above someone in pre-calc =P

 

[SD-Ness]

Thanks, yeah, I managed.

I'll check lambda calculus out, despite my distaste for computer science.

and I think lambda calculus is a *bit* above someone in pre-calc =P

It's a review, fucker. I've already taken a year and a half of calculus.