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  2. The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x -axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x -axis (as x approaches + ∞) and to the left end of the x -axis (as x approaches − ∞).
    www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-end-behavior/a/end-behavior-of-polynomials
    www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f…
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    What are some examples of end behavior?End behavior tells you what the value of a function will eventually become. For example, if you were to try and plot the graph of a function f (x) = x^4 - 1000000*x^2 , you're going to get a negative value for any small x, and you may think to yourself - "oh well, guess this function will always output negative values.".
    How do you find the end behavior of a function?A rational function’s final behavior can take one of three forms: Examine the numerator and denominator degrees. There is a horizontal asymptote of y = 0 y = 0 if the degree of the denominator is greater than the degrees of the numerator, which is the function’s end behavior.
    What is the end behavior of a rational function?The end behavior of a rational function describes how the function f (x) may behave when the input x is a very large positive or negative value. This means determining the behavior of f (x) when x➝∞ or x➝-∞.
    What is the end behavior of a polynomial function when x is very large or very small?Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph. For any polynomial, the end behavior of the polynomial will match the end behavior of the term of highest degree.
     
  4. WEBEnd behavior of the function : Graph of the function : Even : Positive : f (x) → + ∞, as x → − ∞ f (x) → + ∞, as x → + ∞: Example: f (x) = x 2. Even : Negative : f (x) → − ∞, as x → − ∞ f (x) → − ∞, as x → + ∞: Example: f …

  5. WEBPolynomial end behavior is the direction the graph of a polynomial function goes as the input value goes "to infinity" on the left and right sides of the graph. There are four possibilities, as shown below. With end behavior, …

  6. WEBLearn how to identify and describe the end behavior of polynomial functions based on their degree and leading coefficient. See examples, videos, and exercises on polynomial functions and their graphs.

  7. WEBAs we have already learned, the behavior of a graph of a polynomial function of the form. f (x) = anxn +an−1xn−1+… +a1x+a0 f ( x) = a n x n + a n − 1 x n − 1 + … + a 1 x + a 0. will either ultimately rise or fall as x …

  8. WEBFeb 26, 2021 · The Graph of y = x n. The primary goal in this section is to discuss the end-behavior of arbitrary polynomials. By “end-behavior,” we mean the behavior of the polynomial for very small values of x (like −1 …

  9. End Behavior of a Function | Definition, Rules

    WEBNov 21, 2023 · Learn how to describe and find the end behavior of a function, which is how it behaves as the input variable approaches infinity or a limit. See examples of polynomials, power functions, and …

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