Graphing Sine Cosine

Question

Give the equation of the graph of y = 2 cos 3x + 1 after it has been stretched vertically by a factor of 2, flipped upside down, and stretched horizontally by a factor of 2.

Answer 1

The parent equation is y= Acos(bx-c) +d where A= amplitude, b is the period, c is the horizontal shift and d is the vertical shift

flipping over the x axis makes this a -cosine graph so y=2cos(3x) +1 becomes

y= -cos(3x-2) +3