Which transformations are needed to change the parent sine function to y is equal to 1 fourth sine open paren 4 times open paren x plus pi over 6 close paren close paren ?

The coefficient 1/4 outside the sine function compresses its output vertically by a factor of 1/4. The factor 4 multiplying x makes the period 2π/4 = π/2, so the graph is horizontally compressed. Since x + π/6 is inside the function, the graph shifts π/6 units to the left. These transformations match choice A.

AI-written and checked against the verified answer.