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Chapter 4: Q. 3 (page 234)

The graph of a rational function never intersects a _______ asymptote.

Short Answer

Expert verified

The graph of a rational function never intersects a vertical asymptote.

Step by step solution

01

Step 1 Definition for the asymptote:

An asymptote is a straight line that continually approaches a given curve but does not meet it at any finite distance.

They are of three types. They are,

  1. Horizontal asymptote.
  2. Vertical asymptote.
  3. Oblique asymptote.
02

Step 2 The graph of a rational function never intersects a vertical asymptote.

This is because, the vertical asymptotes are the vertical lines which corresponds to the zeros of the denominator of the rational function. At zeros of the denominator the rational function will always have undefined value and hence the graph of a rational function never intersects a vertical asymptote.

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Most popular questions from this chapter

Find the domain of the rational function.

F(x)=3xx-12x2-5x-3

Factor the expression6x2+x-2.

Solve the inequality 3-4x>5. Graph the solution set.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

G(x)=x4-1x2-x

True or False The graph of a rational function may intersect a vertical asymptote.
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