1. ## Graphing

Hey guys,

I just finished answering a thread on graphing and I realized that I am lacking in that area as well.

I'm sure I should know this stuff already, but I don't. So I know how to graph trig and exponential functions when they are shifted and things like that, but how do you graph them when you have a combination? For instance, let's say I wanted to graph:

y = e^(2x) + e^(5x) ...to keep it simple

so i can graph e^2x and e^5x, piece of cake, but graphing their sum, I don't know.

or how about products:

e^x * sinx

or e^x * sinx + e^(3x)cosx

or sin(x + 2)*cos(x - 3)

I was also curious about the applications of graphs in biology, when they talk about "steady state solutions" and their graphs, but i guess i'll leave that for another thread another time.

thanks guys

2. That's an interesting question, have you tried to graph the functions on a graphing calculator ( or any other graphing utility) and then graph their products or sums in the same viewing window and then compare the graphs?

3. Originally Posted by Pupka
That's an interesting question, have you tried to graph the functions on a graphing calculator ( or any other graphing utility) and then graph their products or sums in the same viewing window and then compare the graphs?
no. i'm not the graphing utility kind of guy, in fact, i dont even know how to use a graphng calculator. i much rather doing things by hand, and that's how i want to learn to graph functions like these.

i have seen graphs of functions like these, but i was unable to, at first glance, recognize any helpful similarities between them and the functions i do know how to graph.

4. Originally Posted by Jhevon
no. i'm not the graphing utility kind of guy, in fact, i dont even know how to use a graphng calculator. i much rather doing things by hand, and that's how i want to learn to graph functions like these.

i have seen graphs of functions like these, but i was unable to, at first glance, recognize any helpful similarities between them and the functions i do know how to graph.
This is what I use on the Forum. It has a nice interface.
Graph

-Dan

5. Originally Posted by topsquark
This is what I use on the Forum. It has a nice interface.
Graph

-Dan
ah yes, i am familiar with this program. either you or TPH introduced me to it a while ago. however, as i said, i am interested in learning to graph these functions by hand

6. Originally Posted by Jhevon
Hey guys,

I just finished answering a thread on graphing and I realized that I am lacking in that area as well.

I'm sure I should know this stuff already, but I don't. So I know how to graph trig and exponential functions when they are shifted and things like that, but how do you graph them when you have a combination? For instance, let's say I wanted to graph:
You do that in Calculus I, did for forget?

Find the derivatives, critical points, asymptotes, turning points, infection points, all that stuff.

y = e^(2x) + e^(5x) ...to keep it simple
Find the graph for e^(2x), easy.
FInd the graph for e^(5x), easy.
The new graph is the sum of the coordinates.

e^x * sinx
The only smart about I see is through Calculus.
But I happen to know how it looks even before doing any Calculus on it nor graphing it .

That is a famous curve which appears in unstable vibrational systems.
(Have you done that in Differencial Equations?)