How do you find the domain and range of #y=2sqrtx#?

Answer 1

Domain #x in (0, oo)#
Range #y in (0, oo)#

A function's range is the range of possible y-values (minimum to maximum y-value), and its domain is the entire set of possible values of the independent variable.

Since we are limited to using only rational numbers in this instance, we cannot have a negative x. If we did, we would have an infinite domain and range. Consequently, the range that results for y is also from zero to infinity.

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Answer 2

To find the domain and range of the function ( y = 2\sqrt{x} ):

  1. Domain (input values): The square root function ( \sqrt{x} ) is defined only for non-negative real numbers (since square roots of negative numbers are not real). Therefore, the domain of ( y = 2\sqrt{x} ) is all real numbers greater than or equal to 0. In interval notation, the domain is ([0, \infty)).

  2. Range (output values): Since ( \sqrt{x} ) always yields non-negative values, and multiplying by 2 does not change this property, the range of ( y = 2\sqrt{x} ) will also be non-negative real numbers. In interval notation, the range is ([0, \infty)).

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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.

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.

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.

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.

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