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Home / 05 Polynomial Functions / 06 Polynomial End Behavior

Example: Determine the end behavior of the polynomials:

  • \(P(x) = 13x+\frac{{1}}{{4}}x^2+\frac{{1}}{{2}}x^4\)
    • \(y\rightarrow\) ____ as \(x\rightarrow -\infty\)
    • \(y\rightarrow\) ____ as \(x\rightarrow \infty\)

  • \(P(x) = x(x-2)(x-4)^3\)
      • \(y\rightarrow\) ____ as \(x\rightarrow -\infty\)
      • \(y\rightarrow\) ____ as \(x\rightarrow \infty\)

Solution

  • \(P(x) = 13x+\frac{{1}}{{4}}x^2+\frac{{1}}{{2}}x^4\)
    • \(y\rightarrow \infty\) as \(x\rightarrow -\infty\)
    • \(y\rightarrow \infty \) as \(x\rightarrow \infty\)

  • \(P(x) = x(x-2)(x-4)^3\)
      • \(y\rightarrow -\infty\) as \(x\rightarrow -\infty\)
      • \(y\rightarrow \infty\)as \(x\rightarrow \infty\)