Question

The range of y-sinx is the set of real numbers.
True
False

Answer 1

False

Explanation:

Image (graph) of y = Sinx is attached.

First, lets understand domain and range.

Domain is the set of all x-values for which a function is defined (x axis).

Range is the set of all y-values for which a function is defined (y axis).

We are said that range of y = Sin x is the set of all real numbers.

If we look at the graph and look at the y-values for which the function is defined, we see that the Sin Curve oscillates between y = -1 and y = 1.

So the range would be:

`-1 \leq y \leq 1`

It is not defined for other values, certainly not for ALL REAL NUMBERS!

So, this statement is false.