Which of the following lines are asymptotes of the graph of ^y=(x)/(x+1) I. x=1 II. x=-1 III. y=

Name: Problem 28, Chapter 1: Math Level 2 SAT Subject Test
Uploaded: 2019-08-29T15:51:24-08:00
Duration: 1 min 46 s
Channel: Grant Castaneda
Description: Which of the following lines are asymptotes of the graph of ^y=(x)/(x+1) I. x=1 II. x=-1 III. y=1 (A) I only (B) II only (C) III only (D) I and II (E) II and III

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Question

Which of the following lines are asymptotes of the graph of $^{y=\frac{x}{x+1}}$ I. $x=1$ II. $x=-1$ III. $y=1$ (A) I only (B) II only (C) III only (D) I and II (E) II and III

   Which of the following lines are asymptotes of the graph of $^{y=\frac{x}{x+1}}$
I. $x=1$
II. $x=-1$
III. $y=1$
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

Math Level 2 SAT Subject Test

Richard Ku, Howard… 10th Edition

Chapter 1, Problem 28

Instant Answer

Solved by Expert Grant Castaneda

08/29/2019

Step 1

A vertical asymptote occurs when the denominator of the function is equal to zero. In this case, the denominator is $x+1$. Setting this equal to zero, we get $x=-1$. So, there is a vertical asymptote at $x=-1$. This means that II is correct. Now, let's consider Show more…

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Which of the following lines are asymptotes of the graph of $^{y=\frac{x}{x+1}}$ I. $x=1$ II. $x=-1$ III. $y=1$ (A) I only (B) II only (C) III only (D) I and II (E) II and III

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Key Concepts

Rational Functions

A rational function is a function expressed as the quotient of two polynomials. Its overall behavior, including intercepts and asymptotes, is determined by the degrees and coefficients of the numerator and the denominator.

Vertical Asymptotes

Vertical asymptotes occur at x-values where the denominator of a rational function is zero while the numerator is nonzero. These lines indicate values that the function cannot take and around which the function tends toward positive or negative infinity.

Horizontal Asymptotes

Horizontal asymptotes describe the behavior of a function as x approaches infinity or negative infinity. For rational functions where the degrees of the numerator and denominator are equal, the horizontal asymptote is determined by the ratio of the leading coefficients.

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