Question

what is the range of the function y= 2sinx​

Answer 1

Hello!

The answer is: [-2,2]

Why?

The range of a function shows where the function can exist in the y-axis.

To know the range of the function, we have to isolate x,

So

$y=2sinx\\\frac{y}{2}=sinx\\ Sin^{-1}(\frac{y}{2}) = x$

The only possible values that y can take go from -2 to 2. Taking values out of these values will give as result a non-real number.

Therefore,

The range of  the function is [-2,2]

Have a nice day!

Answer 2

Answer:

The range is (-2,2)

Step-by-step explanation:

The range of  sinx  is 1<inx<1  or −1<y<1

It implies,  

−2<2sinx<2    

This means that the range of  y=2sinx  is  −2<y<2

The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.

y=−2

The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.

y  =2  The range is −2≤y≤2.