Question 1208030
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For each point (a,b) that is on the graph of y = f(x), the point (2a +1, 3b) is plotted, 
forming the graph of another function y = g(x). 
As an example, the point (0,2) lies on the graph of y = f(x), so the point 
(2 • 0 + 1, 3 • 2) = (1, 6) lies on the graph of y = g(x).
(a) Plot the graph of y = g(x). Include the diagram as part of your solution.
(b) Express g(x) in terms of f(x).
(c) Describe the transformations that can be applied to the graph of y = f(x) to obtain the graph of y = g(x). 
For example, one transformation could be to stretch the graph vertically by a factor of 4.
The graph: https://artofproblemsolving.com/texer/gbtdafpj
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        I will solve  (b)  and  (c).    You make the rest.



<pre>
(b)  As the problem describes, we start from the point (a,b) = (a,f(a)).
     
     We transform it into the point (2a+1,g) = (2a+1,3f(a)).


     So,  g(2a+1) = 3*f(a).    (1)


     Now we want to call 2a+1 as new variable x;  so we write

           x = 2a + 1,  which means that  a = {{{(x-1)/2}}}.

  
     Then the equality (1) takes the form

            g(x) = {{{3*f((x-1)/2)}}}.    (2)


     This formula (2) defines function g(x) via function f(x).

      So, formula (2) is the answer to question (b).


      At this point, part (b) is complete.



(c)  Based on formula (2) from part (b), the transformations that can be applied to the graph of y = f(x) 
     to obtain the graph of y = g(x)  are as follows:


         - shift the plot of f(x) 1 unit right;

         - then stretch x-axis with coefficient 2;

         - then stretch y-axis with coefficient 3.
</pre>

Parts (b) and (c) are completed.