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Given that the point $(4,7)$ is on the graph of $y=f(x)$, there is one point that must be on the graph of $2y=3f(4x)+5$. What is the sum of coordinates of that point?

Lightning  Jul 24, 2018
 #1
avatar+87564 
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Given that the point (4,7) is on the graph of y=f(x), there is one point that must be on the graph of 2y=3f(4x)+5. What is the sum of coordinates of that point?

 

2y  = 3f(4x) + 5       divide through by  2

 

y = (3/2) f(4x) + 5/2

 

The  "4x"  part  compresses the graph horizontally by a factor of 4

The "3/2"  part vertically  stretches the graph by a factor  of 3/2

The "5/2"  part  shifts the resulting point up by  5/2 units

 

Applting the first two  to (4,7)  we get  (4*(1/4) , 7* (3/2) ) =  ( 1, 21/2)

 

Applying the last one, we arrive at   ( 1, 21/2 + 5/2)  = (1, 26/2)  = ( 1,13)

 

The sum of the coordinates  is  1 + 13   = 14

 

cool cool cool

CPhill  Jul 24, 2018

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