SOLUTION: Write a function whose graph represents the indicated transformation of the graph of f. f(x)=√x+4; vertical stretch by a factor of 4, followed by a translation 2 units right.

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Question 1080180: Write a function whose graph represents the indicated transformation of the graph of f. f(x)=√x+4; vertical stretch by a factor of 4, followed by a translation 2 units right.
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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Write a function whose graph represents the indicated transformation of the graph of f. f(x)=sqrt(x+4); vertical
stretch by a factor of 4, followed by a translation 2 units right.
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1.  Original function is f(x) = sqrt(x+4) = sqrt%28x%2B4%29  

             (it is how I read your writing, which does not allow me to select between  sqrt(x) + 4  and  sqrt(x+4) ).


2.  After vertical stretch by a factor of 4:  g(x) = 4%2Asqrt%28x%2B4%29.


3.  After a translation 2 units right:  h(x) = 4%2Asqrt%28%28x-2%29%2B4%29 = 4%2Asqrt%28x%2B2%29.

    See the trick I did to translate the plot in 2 units right: I replaced x in the function by (x-2).  That's all.




Plot f(x) = sqrt%28x%2B4%29 (red), g(x) = 4%2Asqrt%28x%2B4%29 (green), and h(x) = 4%2Asqrt%28x%2B2%29 (blue).