The point A(3,0.5) lies on the graph of )(xf . Find the corresponding positionto the point A under the transformationy = 2f (3x)+5

The transformation y = 2f(3x) + 5 involves two operations: a horizontal compression by a factor of 1/3 and a vertical stretch by a factor of 2, followed by a vertical shift upwards by 5 units.

1. Horizontal compression: The x-coordinate of the point is multiplied by 1/3. So, the x-coordinate of the point A(3, 0.5) becomes 3*(1/3) = 1.

2. Substitution into the function: Now we substitute this new x-coordinate into the function f(x). But since the point A lies on the graph of the function, we know that f(3) = 0.5. Therefore, f(1) = 0.5.

3. Vertical stretch and shift: The y-coordinate is first multiplied by 2 and then 5 is added. So, the y-coordinate becomes 2*0.5 + 5 = 6.

Therefore, the corresponding position to the point A under the transformation y = 2f(3x) + 5 is (1, 6).