127k views
1 vote
Attributes of Functions What are the asymptotes of the function f at z+ 2?2+3

A. Vertical asymptote: y = -3; horizontal asymptote: x = 2
B. Vertical asymptote: y = 2; horizontal asymptote: x = -3
C. Vertical asymptote: x = -3; horizontal asymptote: y = 2
D. Vertical asymptote: x = 2; horizontal asymptote: y = -3

1 Answer

4 votes

Final answer:

The correct answer is option B. The function has a vertical asymptote at x = -3 and a horizontal asymptote at y = 2.

Step-by-step explanation:

The correct answer is option B.

To determine the asymptotes of the function, we need to look at its behavior as x approaches infinity and as x approaches negative infinity.

For the vertical asymptote, we need to find the value of x for which the function approaches infinity or negative infinity. In this case, as x approaches negative infinity, the function y = 1/x approaches negative infinity. Therefore, there is a vertical asymptote at x = -3.

For the horizontal asymptote, we need to find the value of y for which the function approaches a constant value as x approaches infinity or negative infinity. In this case, as x approaches infinity, the function y = 1/x approaches 0. Therefore, there is a horizontal asymptote at y = 2.

The correct answer is option D. When determining asymptotes of a function, we look at the behavior of the function as the input (usually x) approaches certain critical values. For a function like f(x) = 1/(x-2) +3, which seems similar to the one described by the question, the vertical asymptote occurs where the function is undefined, which is at x = 2. As x approaches 2 from either direction, the value of f(x) becomes infinitely large or infinitely negative.

The horizontal asymptote is determined by the behavior of the function as x goes to infinity. Since the value of 1/(x-2) approaches 0 as x increases without bound, the y-value approaches the constant term, which is y = -3. So, the function has a horizontal asymptote at y = -3 and a vertical asymptote at x = 2.

User Rsboarder
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories