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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 relative to the x-axis (meaning that all y-coordinates are doubled), the resulting graph is identical to the original graph.

Given that f(0)=1 , what is f(10)?

 Sep 28, 2019
 #1
avatar+681 
+2

Hint: Try to write an equation for the context, and use the given f(0)=1 to find the f(10) or find the f(1) to find the f(10). 

Also,,, if they say that the function has shifted 2 units to the right,,, then that would do something to the x axis wouldn't it... 

From what i have understood they are just asking you to translate a line (if its not exponential) 2 units the right and double the y axis... and they give the y intercept as (0,1). Use the information they have given you, and write an equation for it and solve for f(10). 
Now, im going to leave the rest to you. :)


Correct me if i am wrong please.
smiley
hope this helps in some way. 

 Sep 28, 2019
 #2
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+1

can you explain further?

 Sep 29, 2019
 #3
avatar+107116 
+1

(0,1) is a point on the original graph.

If you move this right two then the x value becomes 0+2=2  and if stretch by a factor of 2 then  the y value beomes  1*2=2

So a point on the translated graph is (2,2)

BUT

(2,2) must also be on the original fucntions.

So what is the equation of the line that goes through   (0,1) and (2,2)   ?

Then you can find f(10)
 

 Oct 4, 2019

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