End behavior of $$$f{\left(x \right)} = - 7 x^{6} + 3 x^{4} - 5 x^{2}$$$

Find the end behavior of $$$f{\left(x \right)} = - 7 x^{6} + 3 x^{4} - 5 x^{2}$$$.

Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is $$$- 7 x^{6}$$$, the degree is $$$6$$$, i.e. even, and the leading coefficient is $$$-7$$$, i.e. negative.

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 $$$x \rightarrow \infty$$$.