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#1 2005-12-15 07:32:07

sarah
Guest

general statements

back with more questions

1. make a general statement about the effect of 'c' on the graph of f(x) = (a^x) + c

2. make a general statement about the effect of 'b' on the graph of f(x) = b * (a^x)

3. make a general statement about the effect of 'k' on the graph of f(x) = a^(k*x)

4.how does the graph of f(x) = a^-x compare to the graph of f(x) = a^x?

thank you!!

#2 2005-12-15 07:35:27

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: general statements

Do you have a graphing calculator?  If not, you can do all these by hand by just plugging in points.

1. Try graphing 2^x + 0, 2^x + 1, and 2^x - 1

2. 1 * (2^x), 2*(2^x), 4*(2^x)

3. 2^(1*x), 2^(2*x), 2^(4*x)

4. 2^x and 2^-x

Just try different ones, and you should very quickly begin to see a pattern emerge.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2005-12-15 08:05:09

Tredici
Member
Registered: 2005-12-12
Posts: 28

Re: general statements

As Ricky said it's always fun to just experiment with these things and see what comes up. Generally you will notice a reoccuring pattern in behaviours.

However, I'm going to jump at this opportunity to actually help someone, thought I'd be the one absorbing all the help around here, not giving it out. smile.

1. vertical translation of +c
2. vertical stretch of scale factor b
3. horizontal compression of scale factor k, also referred to as horizontal stretch of scale factor 1/k.
4. if ƒ(x) = a ^ x and g(x) = a ^ -x, g(x) is a reflection of ƒ(x) in the y axis.

Someone correct me if I'm wrong, don't want to be giving out dummy information!

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#4 2005-12-15 08:58:27

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: general statements

You can try using this Graph Maker.

Example:

1. Enter "x^2+4", and press "PlotF" (bottom left). Then change 4 to 5 (or 3 etc) and press PlotF again to see what happens when "c" changes.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#5 2005-12-17 12:53:05

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,562

Re: general statements

Nice job on the Graph Maker applet!  I was examining the hyperbolic functions.
They are still a mystery to me, but I see the basic shape now.


igloo myrtilles fourmis

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#6 2005-12-17 17:36:35

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: general statements

A guy callled Patrik Lundin actually wrote it.

But I have been thinking about writing one in Flash, so that I can extend it.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#7 2005-12-17 19:01:06

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: general statements

For the hyperbolic functions:
Why does the chain has an equation


IPBLE:  Increasing Performance By Lowering Expectations.

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