Find the equation of the graph given below. Notice that the sine function is used in the answer template, representing a sine function that is shifted and/or reflected. Use the variable x in your equation, but be careful not use the multiplication x symbol.

y= __sin(___)+__

y = 2sin(x/2 - pi/4) + 1

Step-by-step explanation:

The normal sine has a range of [-1, 1]. This one has a range of [-1, 3], so the amplitude is 2 times higher (4 vs 2).

After that, 2sin(x) has a range of [-2, 2], but this one has a range of [-1, 3], so we need to shift it upwards by 1.

We now know that the answer is 2sin(____)+1.

A normal sine has it's middle point while rising at x = 0, but this one has it at x = pi/2 - so we need to shift a sine to the right by pi/2.

Lastly, a sine has a cycle of length 2pi, but this one has a cycle of length 4pi. We can achieve that by dividing the argument 2.

We now know that the answer is 2sin(x/2 - pi/4) + 1. We can plot it to verify.

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