Question

Select the correct statements for the given graph of $y=5\sin (x+\frac{\pi }{4})\forall x\in R.$

• A. Period $=\frac{5\pi }{4}$
• B. Period $=2\pi$
• C. $y=0\text{at}x=-\frac{\pi }{4},\frac{3\pi }{4}$
• D. Range $=[-5,5]$

Answer 1

Answer: (B), (C), (D)

Range $=[-5,5]$

Given the graph of the function as shown:
The graph repeats itself after every $2\pi$ interval. Therefore the period of the function is $2\pi$.

We can also see that minimum value of function is $-5$ and maximum value of function is $5$, therefore the range of the function is $[-5,5]$.

$y=0\text{in}x\in [-\pi ,\pi ]$ when $x=-\frac{\pi }{4},\frac{3\pi }{4}$