Question

Part A: Explain how to determine the value of the vertical translation, d, for the graph of g(x). (2 points)

Part B: Explain how to determine the value of the vertical translation, d, for the graph of f(x) = 2sin(θ + 120°) + 6. (3 points)

Answer 1

Part A: Up 9

Part B: Up 6

Explanation:

Part A: The graph appears to be a cosine graph since it starts at a peak on the y-axis. Normally a cosine graph starts at (0,1). This graph begins at (0,10). It has been shifted up y a translation by 9.

Part B: Each trig equation has a basic structure f(x) = a sin (x+b) + k where:

• a is the vertical stretch
• b is the horizontal shift
• k is the vertical shift

A vertical translation is a vertical shift and is represented by the value in k added outside of the function. In the equation f(x) = 2sin(θ + 120°) + 6, k = 6. The vertical translation is 6.