# C3 Graph Transformation Help!Watch

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#1
Simple question: How do you transform the graph f(x) = e^x to f(x) = e^kx?
I thought you had to stretch it by factor e^k in the x-direction but it's actually by factor 1/k. Don't understand why this is
2
8 years ago
#2
You're making the independent variable increase k times as fast, so you squish it. You can check it for x=1, the old f(x) will be e, the new will be e^k, so for k>1 it will have shot up faster, for k<1 it will be a slower increase.
0
8 years ago
#3
For a function f(x), f(kx) will stretch it parallel to the x-axis with scale factor 1/k.

If you can't remember the transformations, try considering the graphs of (for translations and reflections) and for stretches. Works for me.

(You seem to have got negged for no reason, so here's a free rep back )
1
8 years ago
#4
(Original post by gildartz)
Simple question: How do you transform the graph f(x) = e^x to f(x) = e^kx?
I thought you had to stretch it by factor e^k in the x-direction but it's actually by factor 1/k. Don't understand why this is
The reason is that for every x value in the new function, the value of kx is k times larger than the value of x in f(x)=e^x. This means that the new x inputs need to be k times smaller to produce the same outputs as before.

This results in a stretch of scale factor 1/k parallel to the x axis.
0
#5
Ah I see, thanks for the help everyone

(Original post by Goldfishy)
For a function f(x), f(kx) will stretch it parallel to the x-axis with scale factor 1/k.

If you can't remember the transformations, try considering the graphs of (for translations and reflections) and for stretches. Works for me.

(You seem to have got negged for no reason, so here's a free rep back )
Haha, thanks for the rep, you can have some yourself
0
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