Final answer:
The equation of the transformed graph of sine with a period that has been shifted vertically up 3 units and has an amplitude is f(x) = sin(x) + 3.
Step-by-step explanation:
The equation of the transformed graph of sine with a period that has been shifted vertically up 3 units and has an amplitude of _____ is
A) f(x) = sin(x) + 3
B) f(x) = 3sin(x)
C) f(x) = sin(x - 3)
D) f(x) = sin(x) - 3
The correct answer is A) f(x) = sin(x) + 3. This equation represents a vertical shift up of 3 units from the original graph of sine, while also maintaining the same amplitude.
The student has asked to write the equation of a transformed sine graph which has been shifted vertically up 3 units and has an unspecified amplitude.
The correct option for such a transformation would involve adding the vertical shift to the sine function. Since we are only given information about a vertical shift and no change to amplitude or period, the equation A) f(x) = sin(x) + 3 is the correct choice because it shows the graph of sine that is shifted vertically upwards by 3 units.