Question

find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the rational function.

(f(x) = \frac{x}{x^2 + 17})

select the correct choice below and, if necessary, fill in the answer box to complete your choice. (type an integer or a fraction. use a comma to separate answers as needed.)

a. the vertical asymptote(s) is (are) (x =) . there are no holes.
b. there are no vertical asymptotes but there is (are) hole(s) corresponding to (x =) .
c. the vertical asymptote(s) is (are) (x =) and hole(s) corresponding to (x =) .
d. there are no discontinuities.

Explanation:

Analyze the denominator for domain exclusions

Using the Vertical Asymptotes Determination and Rational Function Holes knowledge points

$$
LATEXBLOCK0
$$

Determine real discontinuities

Using the Domain Exclusion knowledge point

$$
LATEXBLOCK1
$$

Identify asymptotes and holes

Using the Vertical Asymptotes Determination and Rational Function Holes knowledge points

$$
LATEXBLOCK2
$$

Answer:

• A. The vertical asymptote(s) is (are) \(x =\) [blank]. There are no holes.
• B. There are no vertical asymptotes but there is (are) hole(s) corresponding to \(x =\) [blank].
• C. The vertical asymptote(s) is (are) \(x =\) [blank] and hole(s) corresponding to \(x =\) [blank].
• D. There are no discontinuities. (Correct answer)