Question

Correct graph of the equation $y=\sin \left(|x+\frac{\pi }{4}|\right)-3$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

To draw the graph of $y=\sin \left(|x+\frac{\pi }{4}|\right)-3$, we need to apply transformations to fundamental function $\sin x$.

Graph of $\sin x$ is given by
Now apply the horizontal shift to get $y=\sin (x+\frac{\pi }{4})$ as shown below


Now apply the vertical flip to get $y=\sin \left(|x+\frac{\pi }{4}|\right)$ as shown below



Now apply the horizontal shift by 3 units to get $y=\sin \left(|x+\frac{\pi }{4}|\right)-3$ as shown below

As we can see, option (c) is correct graph of $y=\sin \left(|x+\frac{\pi }{4}|\right)-3$