Question 1080180
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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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<pre>
1.  Original function is f(x) = sqrt(x+4) = {{{sqrt(x+4)}}}  

             (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*sqrt(x+4)}}}.


3.  After a translation 2 units right:  h(x) = {{{4*sqrt((x-2)+4)}}} = {{{4*sqrt(x+2)}}}.

    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.
</pre>


{{{graph( 330, 330, -6.5, 10.5, -1.5, 20.5,
          sqrt(x+4), 4*sqrt(x+4), 4*sqrt(x+2)
)}}}


Plot f(x) = {{{sqrt(x+4)}}} (red), g(x) = {{{4*sqrt(x+4)}}} (green), and h(x) = {{{4*sqrt(x+2)}}} (blue).