Which of the following transformations appears to be a translation of the graph of $y=\sin \left(x\right)$?

• A. $y=2\sin \left(x\right)$
• B. $y=-\sin \left(x\right)$
• C. $y=\sin \left(2x\right)$
• D. $y=\sin (x+2)$

Answer: (D)

Verified step by step guidance

1. Recall that a translation of the graph of a function involves shifting the graph horizontally or vertically without changing its shape or orientation.
2. Examine the given transformations and identify what each one does to the graph of \(y = \sin(x)\):
3. 1. \(y = 2\sin(x)\) changes the amplitude (vertical stretch), so it is not a translation.
4. 2. \(y = -\sin(x)\) reflects the graph across the x-axis, which is a reflection, not a translation.
5. 3. \(y = \sin(2x)\) changes the period (horizontal compression), so it is not a translation.
6. 4. \(y = \sin(x + 2)\) shifts the graph horizontally to the left by 2 units, which is a horizontal translation.