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Exercises Polynomials and factoring

Example 1 from Algebra and Trigonometry, 5.6 Rational Functions

Using Arrow Notation

Use arrow notation to describe the end behavior and local behavior of the function graphed in Figure 6.

Graph of f(x)=1/(x-2)+4 with its vertical asymptote at x=2 and its horizontal asymptote at y=4.

Figure 6

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
Notice that the graph is showing a vertical asymptote at $x = 2,$ which tells us that the function is undefined at $x = 2.$

$As x \to 2^{-}, f (x) \to - \infty, and as x \to 2^{+}, f(x)\to\infty.$

And as the inputs decrease without bound, the graph appears to be leveling off at output values of 4, indicating a horizontal asymptote at $y = 4.$ As the inputs increase without bound, the graph levels off at 4.

$As x \to \infty, f(x)\to4$

Your turn

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

Use arrow notation to describe the end behavior and local behavior for the reciprocal squared function.

How did it go?

PreviousSolving Polynomial Equations Next Using Transformations to Graph a Rational Function

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.6, 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.