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The graph of a sine function g(x) is presented below.

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

Part B: Explain how to determine the value of the vertical translation, d, for the graph of f(x) = 9sin(θ + 60°) + 6. 

 May 3, 2023
 #1
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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.

 May 4, 2023

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