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Exercises Polynomials and factoring

Example 3 from Algebra and Trigonometry, 5.2 Power Functions and Polynomial Functions

Identifying the End Behavior of a Power Function.

Describe the end behavior of the graph of $f (x) = - x^{9} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The exponent of the power function is 9 (an odd number). Because the coefficient is $–1$ (negative), the graph is the reflection about the $x -$ axis of the graph of $f (x) = x^{9} .$ Figure 6 shows that as $x$ approaches infinity, the output decreases without bound. As $x$ approaches negative infinity, the output increases without bound. In symbolic form, we would write

$\begin{array}{l} as x \to - \infty, f (x) \to \infty \\ as x \to \infty, f (x) \to - \infty \end{array}$

Figure 6

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Describe in words and symbols the end behavior of $f (x) = - 5 x^{4} .$

How did it go?

PreviousIdentifying the End Behavior of a Power Function Next Identifying Polynomial Functions

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.