SOLUTION: Determine the domain and range of the function Y=-4cos3/2(x-1)+3

Question 1161122: Determine the domain and range of the function Y=-4cos3/2(x-1)+3
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The domain of any sinusoidal function is all real numbers.

The "3/2" coefficient on the cosine function changes the period; it has no effect on the range.

The "x-1" causes a phase (horizontal) shift; it also has no effect on the range.

The "-4" expands the graph vertically, so it does affect the range.

The "+3" shifts the graph vertically, so it also affects the range.

The basic cosine function oscillates between -1 and 1.
The "-4" coefficient changes the range to between -4 and 4.
The "+3", since it moves the whole graph up 3, changes the range to between -1 and 7.

ANSWERS:
Domain: all reals
Range: [-1,7]

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