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When the graph of a certain function $f(x)$ is shifted $2$ units to the right and stretched vertically by a factor of $2$ (meaning that all $y$-coordinates are doubled), the resulting figure is identical to the original graph. Given that $f(0)=0.1$, what is $f(10)$?

michaelcai  Aug 25, 2017
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5+0 Answers

 #1
avatar+90130 
+3

When the graph of a certain function f(x) is

shifted 2 units to the right

and stretched vertically by a factor of 2 (meaning that all y-coordinates are doubled), the resulting figure is identical to the original graph. Given that f(0)=0.1, what is f(10)?

 

f(x)=2f(x-2)

 

 

\(Given\qquad f(0)=0.1 \qquad find \;\;f(10)\\ f(x)=2f(x-2)\\ f(2)=2f(2-2)=2*f(0)=2*0.1=0.2\\ f(4)=2f(4-2)=2*f(2)=2*0.2=0.4\\ f(6)=2f(6-2)=2*f(4)=2*0.4=0.8\\ f(8)=2f(8-2)=2*f(6)=2*0.8=1.6\\ f(10)=2f(10-2)=2*f(8)=2*1.6=3.2\\~\\ f(10)=3.2 \)

Melody  Aug 26, 2017
 #2
avatar+76069 
+1

 

Thanks, Melody.....I had no clue on this one.....!!!!

 

 

cool cool cool

CPhill  Aug 26, 2017
 #3
avatar+1088 
+1

I'm glad I am not the only one...

TheXSquaredFactor  Aug 26, 2017
 #4
avatar+90130 
+1

I think I saw Rom or Bertie do one one time. 

I thought it was quite entriguing. :)

Melody  Aug 27, 2017
 #5
avatar+90130 
+1

I've been thinking more about this question.

 

When the graph of a certain function f(x) is

shifted 2 units to the right

and stretched vertically by a factor of 2 (meaning that all y-coordinates are doubled), the resulting figure is identical to the original graph. Given that f(0)=0.1, what is f(10)?

 

From my previous answer I have:

x0246810
f(x)0.10.20.40.81.63.2

 

These points satisfy the equation

 \(f(x)=0.1*2^{(n/2)}\)

 

I graphed this to check it worked properly.   It did :)

https://www.desmos.com/calculator/ugcl3yupfo

 

 

 

I am almost sure that if I think about it hard enough I could learn something more about transformations from this question ......

Melody  Aug 28, 2017

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