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The graph of y=f(x) is shown below.





The graph of y=g(x) is shown below.



What is g(x) in terms of f(x)? For example, if you think g(x)=f(x)+1 enter " f(x)+1", without quotation marks.

 

Thanks, and does use locating points on the graph?

 Dec 9, 2018
 #1
avatar+101778 
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Note that the point (2, 0) is on f(x)

And the corresponding point on g(x) is (4, - 4)

 

So g(x)   is  the graph of  f(x) shifted down 4 units  and vertically " stretched" by a factor of 2

 

So

 

g(x) =  f(2x) - 4

 

 

cool cool cool

 Dec 9, 2018
 #2
avatar+4296 
+1

Close...

We can obtain the graph of \(y=g(x)\) by taking the graph of \(y=f(x)\) and stretching it horizontally by a factor of 2, then shifting it down by 4 units. Therefore, \(g(x) = \boxed{f \left( \frac{x}{2} \right) - 4}.\)

 

Isn't this correct?

tertre  Dec 9, 2018

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