Chapter 1: Q 7. (page 86)

If $\lim_{x \to - \infty} f (x) = \infty$ , $\lim_{x \to \infty} f (x) = 3$ , and $\lim_{x \to - 1^{+}} f (x) = \infty$ , what can you say about any horizontal and vertical asymptotes of $f$ ?

Short Answer

Expert verified

The horizontal asymptote at $y = 3$ and the vertical asymptote at $x = 1$ .

Step by step solution

Step 1. Given information.

It is given that $\lim_{x \to - \infty} f (x) = \infty$ , $\lim_{x \to \infty} f (x) = 3$ and $\lim_{x \to 1^{+}} f (x) = \infty$ .

Step 2. Find any horizontal and vertical asymptotes of f.

From the given expression $\lim_{x \to \infty} f (x) = 3$ , for any value of $x$ , the functional value is $3$ i.e., $f (x) = 3$ is a horizontal line.

So, $f$ has a horizontal asymptote at $y = 3$ .

Again, for the expression role="math" localid="1648312358902" $\lim_{x \to 1^{+}} f (x) = \infty$ at $x = 1$ the function have a vertical line.

So, $f$ has a vertical asymptote at $x = 1$ .

Step 3. Simplified answer.

The horizontal asymptote at $y = 3$ and the vertical asymptote at $x = 1$ .

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If $\lim_{x \to - \infty} f (x) = \infty$ , $\lim_{x \to \infty} f (x) = 3$ , and $\lim_{x \to - 1^{+}} f (x) = \infty$ , what can you say about any horizontal and vertical asymptotes of $f$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find any horizontal and vertical asymptotes of f.

Step 3. Simplified answer.

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If limx→-∞f(x)=∞, limx→∞f(x)=3, and limx→-1+f(x)=∞, what can you say about any horizontal and vertical asymptotes off?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find any horizontal and vertical asymptotes of f.

Step 3. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

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If $\lim_{x \to - \infty} f (x) = \infty$ , $\lim_{x \to \infty} f (x) = 3$ , and $\lim_{x \to - 1^{+}} f (x) = \infty$ , what can you say about any horizontal and vertical asymptotes of $f$ ?