End Behavior of Functions

The end behavior of a function describes how the function behaves as the input values approach positive or negative infinity.

End behavior refers to the values that a function approaches as the input (x) approaches positive or negative infinity.

It means that as x approaches negative infinity, the function f(x) increases without bound.

It means that as x approaches positive infinity, the function f(x) decreases without bound.

The end behavior of a polynomial function can be determined by the leading term of the polynomial.

The leading term is $$x^4$$ .

As @@x ightarrow- ext{infinity} $$,$$ f(x) ightarrow+ ext{infinity} $$and as$$ x ightarrow+ ext{infinity} $$,$$ f(x) ightarrow+ ext{infinity}@@.

As @@x ightarrow- ext{infinity} $$,$$ f(x) ightarrow+ ext{infinity} $$and as$$ x ightarrow+ ext{infinity} $$,$$ f(x) ightarrow- ext{infinity}@@.

The degree of a polynomial indicates the highest power of x, which influences whether the end behavior goes to positive or negative infinity.

Both ends of the graph will rise to positive infinity: as @@x ightarrow- ext{infinity} $$,$$ f(x) ightarrow+ ext{infinity} $$and as$$ x ightarrow+ ext{infinity} $$,$$ f(x) ightarrow+ ext{infinity}@@.