End Behavior Calculator

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

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 the graphing calculator.

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