What is the domain of #y = 2sinx+ 1#?

Answer 1

The domain of the sine function is all Real numbers, or #(\infty,\infty)#.

That means that this function will continue to repeat its values infinitely to the left and right along the x-axis. (see graph)

It might be beneficial to talk about the range of this function. The normal sine function graph oscillates between -1 and 1. Written in interval notation, this would be #[-1,1]#.

This function, y = 2sin(x) + 1 has undergone a vertical stretch (multiplied by 2) as well as a vertical translation of up 1. Look at the graph to see the new minimum and maximum of -1 and 3. Thus, the range is [-1,3].

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Answer 2

Serenity Jones

The domain of the function y = 2sin(x) + 1 is all real numbers. Since sine function is defined for all real numbers, there are no restrictions on the values of x that can be plugged into the function. Therefore, the domain of y = 2sin(x) + 1 is (-∞, ∞), which means that any real number can be inputted into the function.

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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.