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lim x->-infinity f(x) = -infinity

Definition

The limit of a function as x approaches negative infinity is negative infinity. This means that as x gets infinitely small and approaches negative infinity, the value of the function also becomes infinitely small and approaches negative infinity.

Analogy

Imagine you are driving on a long road that stretches to the left forever. As you keep driving to the left, your car's fuel gauge keeps decreasing without any limit. It goes down and down until it reaches negative infinity, indicating that you have an infinite amount of fuel left.

Related terms

Leading Term: The leading term in a polynomial function is the term with the highest degree. It determines the behavior of the function for large values of x.

Asymptotic Behavior: The asymptotic behavior describes how a function behaves as x approaches positive or negative infinity. It can be determined by analyzing the leading term of a function.

Limit: A limit is a fundamental concept in calculus that describes what happens to a function as its input (x) approaches a certain value or goes towards positive or negative infinity.