What is the end behavior of the square root function?

Answer 1

The square root function #f(x)=sqrtx# has domain #[0,+oo)# and the end behaviour is

as #x->0# , #f(x)->0#

as #x->oo# , #f(x)->oo#

Note: "end behavior" of a function is referred to the behavior of a function when it reaches towards its extreme points.

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Answer 2

Benjamin Achtenberg

The end behavior of the square root function ( f(x) = \sqrt{x} ) as ( x ) approaches positive infinity is that ( f(x) ) increases without bound. As ( x ) approaches negative infinity, the function is undefined in the real number system because the square root of a negative number is not a real number. Therefore, the square root function ( f(x) = \sqrt{x} ) is only defined for ( x \geq 0 ).

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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.