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# Sketching graph logariths/exponential C3 Watch

1. I want to sketch y=4e^-2x

How would I do it? I know how the basic y=e^x looks, but I dont understand what you do when you have a negative power.
2. (Original post by Alex-Torres)
I want to sketch y=4e^-2x

How would I do it? I know how the basic y=e^x looks, but I dont understand what you do when you have a negative power.
Let f(x)=e^x

4f(x)=4e^x

4f(-x)=4e^-x

4f(-2x)=4e^-2x

Can you see what I've just done? Now all you have left to do is apply transformations to go through

f(x)-->4f(x)-->4f(-x)-->4f(-2x)
3. (Original post by Alex-Torres)
I want to sketch y=4e^-2x

How would I do it? I know how the basic y=e^x looks, but I dont understand what you do when you have a negative power.
Personally I would forget about transformation rules, and think about the behaviour of this function.

When x = 0, y = 4 so you can mark the point (0, 4) on the y-axis.

As x gets bigger and bigger, e^(-2x) gets smaller and smaller. However, e^(something) is never zero, whatever 'something' is, so the graph will never touch the x-axis. So from the point (0,4) you can draw a gently sloping curve downwards that approaches the positive x-axis as an asymptote.

For x < 0 , e^(-2x) is positive and increasing as x gets more and more negative, so your curve extends upwards to infinity as x becomes more negative.

To complete the analysis properly, differentiate y to reassure yourself that there are no turning points on the graph.

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Updated: August 16, 2013
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