End behavior
how a graph behaves as it approaches positive or negative infinity
End behavior refers to the behavior of a mathematical function as its input variable (usually denoted by x) increases or decreases without any limit. The end behavior of a function is typically described using its leading term or highest power of x.
For example, consider the function f(x) = 3x^4 – 5x^3 + 2x^2 – x + 7. As x increases without any limit, the dominant term in this function is the leading term 3x^4. So, the end behavior of this function is that it increases without bound and moves to positive infinity. Similarly, as x decreases without any limit, the dominant term in this function is also 3x^4. So, the end behavior of this function is that it decreases without bound and moves to negative infinity.
In general, if the leading term of a polynomial function with positive coefficients has an even degree, then its end behavior is the same for both positive and negative x: the function moves to positive infinity as x increases and moves to positive infinity as x decreases. If the leading term of a polynomial function with positive coefficients has an odd degree, then its end behavior is opposite for positive and negative x: the function moves to positive infinity as x increases and moves to negative infinity as x decreases.
It is important to understand the end behavior of a function because it can give you insights into its long-term behavior and help you understand its characteristics such as the range, domain, and intercepts.
More Answers:
Understanding Average Rate of Change in Math: Definition and ExamplesHow to Approximate Zeros or Roots of a Function: Steps and Methods
Maximizing Your Calculus Potential with the Intermediate Value Theorem