# End Behavior Calculator

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

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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 $x^{4}$, 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.

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