End Behavior Calculator

This calculator will determine the end behavior of the given polynomial function, with steps shown.

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Your Input

Find the end behavior of $$$f{\left(x \right)} = x^{4} - 5 x^{3} + 4 x^{2} + 7 x + 1$$$.

Solution

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is $$$x^{4}$$$, then the degree is $$$4$$$, i.e. even, and the leading coefficient is $$$1$$$, i.e. positive.

This means that $$$f{\left(x \right)} \rightarrow \infty$$$ as $$$x \rightarrow -\infty$$$, $$$f{\left(x \right)} \rightarrow \infty$$$ as $$$x \rightarrow \infty$$$.

For the graph, see graphing calculator.

Answer

$$$f{\left(x \right)} \rightarrow \infty$$$ as $$$x \rightarrow -\infty$$$, $$$f{\left(x \right)} \rightarrow \infty$$$ as $$$x \rightarrow \infty$$$.