How do you find the domain and range of $y = sin(2x)$ ?

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Answer 1 · 2017-10-25T11:06:24

Domain: $(-oo, +oo)$
Range: $[-1, +1]$

$y=sin(2x)$

$y$ is defined $forall x in RR$

$:.$ the domain of $y$ is $(-oo, +oo)$

Let $theta = 2x$

$y = sin theta -> -1<= y <= +1 forall theta in RR$

Hence, $y = sin(2x) -> -1<= y <= +1 forall theta in RR$

$:.$ the range of $y$ is $[-1, +1]$

We can observe the domain and range of $y$ from the graph of #y=sin(2x) below.

graph{sin(2x) [-6.25, 6.234, -3.12, 3.124]}

Answer 2 · 2017-10-25T11:10:49

Domain: $-oo < x < oo or x| (-oo ,oo)$
Range: $−1 ≤ y≤ 1 or [-1.1]$

$y=sin(2x)$ , the domain of the function y=sin(2x) is all real

numbers (sine is defined for any angle measure),

i.e $-oo < x < oo or x| (-oo ,oo)$

The range is $−1 ≤ y≤ 1 or [-1.1]$ , as maximum and minimum

value of $y$ lie in between $-1$ and $1$ , inclusive.

Domain: $-oo < x < oo or x| (-oo ,oo)$

Range: $−1 ≤ y≤ 1 or [-1.1]$

graph{sin(2x) [-10, 10, -5, 5]} [Ans]

How do you find the domain and range of y = sin(2x)y = sin(2x)?