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How do you find the domain and range of #f(x) =2sinx#?

Answer 1

Eli Assouline

Domain : #-oo<=x<=+oo#
Range: #-2<=f(x)<=2#

The value of x in the equation #y=2 sin x# can any real number along the x-axis so the domain is #-oo<=x<=+oo#

The value of f(x) in the equation #y=2 sin x# can only take values from -2 to +2. The range is #-2<=f(x)<=2#

the graph of #f(x)=2 sinx # at close up graph{y=2 sin x[-5,5,-2.5,2.5]}

the graph of #f(x)=2 sinx # at somewhere away graph{y=2 sin x[-20,20,-10,10]}

Blessings...I hope this clarification is helpful.

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Answer 2

Kennedy Adams

To find the domain of ( f(x) = 2\sin(x) ), note that the sine function is defined for all real numbers. So, the domain of ( f(x) ) is all real numbers, or ((-∞, ∞)).

To find the range, since the amplitude of the sine function is 2, the range of ( f(x) ) is from -2 to 2, inclusive, or ([-2, 2]).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.