Questions: Identify any horizontal or vertical asymptotes in the graph. State the domain of f . A. The function has one horizontal asymptote, y=5. (Type an equation) B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is . (Type equations.) c. The function has no horizontal asymptotes. Determine the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, x=3. (Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is (Type equations:) C. The function has no vertical asymptotes. State the domain of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. D=x x< (Type an integer or a fraction.) B. D=x x ≠ (Type an integer or a fraction. Use a comma to separate answers as needed.) c. D=x x ≥ b. (Type an integer or a fraction.) D. The domain is all real numbers.

Identify any horizontal or vertical asymptotes in the graph. State the domain of f . A. The function has one horizontal asymptote, y=5. (Type an equation) B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is . (Type equations.) c. The function has no horizontal asymptotes. Determine the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, x=3. (Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is (Type equations:) C. The function has no vertical asymptotes. State the domain of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. D=x x< (Type an integer or a fraction.) B. D=x x ≠ (Type an integer or a fraction. Use a comma to separate answers as needed.) c. D=x x ≥ b. (Type an integer or a fraction.) D. The domain is all real numbers.
Transcript text: Identify any horizontal or vertical asymptotes in the graph. State the domain of f . A. The function has one horizontal asymptote, $y=5$. (Type an equation) B. The function has two horizontal asymptotes. The top asymptote is $\square$ and the bottom asymptote is $\square$ . (Type equations.) c. The function has no horizontal asymptotes. Determine the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, $x=3$. (Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is $\square$ and the rightmost asymptote is $\square$ (Type equations:) C. The function has no vertical asymptotes. State the domain of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $D=\{x \mid x<$ $\square$ (Type an integer or a fraction.) B. $D=\{x \mid x \neq$ $\square$ (Type an integer or a fraction. Use a comma to separate answers as needed.) c. $D=\{x \mid x \geq$ $\square$ b. (Type an integer or a fraction.) D. The domain is all real numbers.
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Solution

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Solution Steps

Step 1: Find the horizontal asymptote

The graph becomes flat as $x$ approaches positive or negative infinity, approaching the horizontal line $y=5$.

Step 2: Find the vertical asymptote

The graph tends towards infinity as $x$ approaches $3$. The function is undefined at $x=3$, indicating a vertical asymptote at $x=3$.

Step 3: State the domain

The function is defined for all real numbers except $x=3$ where the vertical asymptote is present. Therefore, the domain is $(-\infty, 3) \cup (3, \infty)$.

Final Answer:

Horizontal Asymptote: $y=5$ Vertical Asymptote: $x=3$ Domain: $\{x|x\ne 3\}$ or $(-\infty, 3) \cup (3, \infty)$

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