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Given that the point (9,7) is on the graph of y=f(x), there is one point that must be on the graph of $2y=\frac{f(2x)}2+2$. What is the sum of coordinates of that point?

 Feb 13, 2022
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We first divide 2y = f(2x)/2 + 2 by 2 to get y = f(2x)/4 + 1.  Next we graph the point (9,7).  Then we scale towarards the y-axis by a factor of 2 giving us the point (9,7/2).  Next we scale towards the x-axis by a factor of 4 giving us (9/4,7/2).  Lastly, we translate in the positive y-direction (up) by 1 giving us (13/4,7/2).

 

The answer is then 13/4 + 7/2 = 27/4.

 Feb 13, 2022

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