Question

The graph of y = -3sin( 2x) is shifted to the left by 30 units and up 5 units. Write the new equation.

Answer 1

If the graph has shifted up 5 units, the graph becomes y = -3sin(2x) + 5

Compare y = sin 2x to y = -3sin (2x) + 5 (forget the 5 for now)

shift y = -3 sin (2x) by 30 units to the left, the x-coordinate is -30.
The graph now starts x = -30, y = 0

-3sin ([2*-30] = 0
-3sin(-60) = 0
But this is incorrect, therefore we need to add a constant to make it that -3sin(-60 + C) = 0

therefore -3sin(-60+60) = 0

Which is represented as -3sin(2x+60)

the final equation is y = 5 - 3 sin (2x + 60)