Question

Identify the function which is formed when the following transformations are made on the graph of the function $y=\sin x$
1) Flipped over the y-axis
2) Shifted vertically upwards by 2 units
3) Stretched by a factor of 3 along the x-axis

• A. $y=\sin \left(\frac{x}{2}\right)+3$
• B. $y=\sin \left(\frac{-x}{3}\right)+2$
• C. $y=2\sin \left(\frac{x}{3}\right)$
• D. $y=3\sin \left(\frac{-x}{2}\right)$

Answer 1

The correct option is B $y=\sin \left(\frac{-x}{3}\right)+2$

If we have a function $y=f\left(x\right)$ and we flip its over the y-axis, we get the graph of $y=f(-x)$.
When this graph is shifted upwards by 2 units we get the graph of $y=f(-x)+2$
When this graph stretches by 3 units along the x-axis we get the graph of $y=f\left(\frac{-x}{3}\right)+2$
Here $f\left(x\right)=\sin x$
Hence the correct option is $y=\sin \left(\frac{-x}{3}\right)+2$