+1245 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?
+129852 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
