Question

The function y=sinx has been transformed. It now has amplitude of 5.0, a period of 26, a phase shift of 2 units to the right, a vertical translation of 6.5 units down, and is reflected over the x-axis. Given that (π/6,1/2) is a point in the parent function, use mapping notation to determine the x-coordinate of its image point in the transformed function.

Enter the numerical value of the x-coordinate only in the box below rounded to two decimals.

Answer 1

Start with y = sinx
It now has amplitude of 5.0 : y = sinx ----> y = 5sinx
a period of 26: y = 5sinx ----> y = 5 sin (πx/13)
a phase shift of 2 units to the right: y = 5sin (π/13x) ---> y = 5sin (π/13(x-2))
a vertical translation of 6.5 units down: y = 5sin (π/13(x-2)) ---> y = 5sin (π/13(x-2)) - 6.5
reflected over the x-axis: y = 5sin (π/13(x-2)) - 6.5 ---->y = -5sin (π/13(x-2)) + 6.5