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Exercises Polynomials and factoring

Example 2 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 $f (x) = x^{8} .$

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 coefficient is 1 (positive) and the exponent of the power function is 8 (an even number). As $x$ approaches infinity, the output (value of $f (x)$ ) increases without bound. We write as $x \to \infty, f (x) \to \infty .$ As $x$ approaches negative infinity, the output increases without bound. In symbolic form, as $x \to - \infty, f (x) \to \infty .$ We can graphically represent the function as shown in Figure 5.

Figure 5

How did it go?

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

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.