Question

Which of the following describes the translation of the graph y = sin (x + 1) - 1 with respect to y = sin x?

Answer 1

According to the question, the reference graph is the one of the function y = sin x.

We can see that one unit was added to x in the argument:

`\sin (x+1)`

But also, 1 was subtracted from the whole function:

`\sin (x+1)-1`

Adding 1 to the x inside the argument of the sine function will move the graph one unit to the left. Finally, subtracting 1 to the whole function will move the graph one unit down.

Then, the correct answer is the first option.