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The graph of the exponential function f(x) is shown below. Find f(x).
f(0) = 1 and f(1) = 2.

 May 2, 2024
 #1
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I think you are missing the graph that shows the graph of the exponential function. 

 

However, I can make a geuss to what the exponential function is using the two points :). 

 

Exponential functions are usually in the form of \(y=ax^b\) where a is the y intercept and b is the growth factor. 

 

With the two points you provided, f(0) = 1 is defintely the y intercept at point (0, 1), meaning the a value is 1. 

 

My best geuss at what the growth factor is would probably be that the y value doubles everytime x increases by 1, because that would make the most sense for a exponential function.

 

This would mean the b value or growth factor is 2. 

 

So, my best geuss without a graph of what f(x) is would probably be \(f(x) = 2^x\)

 

I'm not sure if it's right, but it does satisfy the two points given, and that was all, so I hope it was a bit helpful!

 

Thanks!

 May 2, 2024

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