The Graph of the Function $f ( x ) = \frac { 3 x } { x + 1 }$

question 21

Multiple Choice

The graph of the function $f ( x ) = \frac { 3 x } { x + 1 }$ is shown below. Determine the vertical and horizontal asymptotes of its graph.

• A) \(\text { horizontal: } y = - 1 \text {; vertical } x = 3\)
• B) \(\text { horizontal: } y = 3 \text {; vertical } x = - 3\)
• C) \(\text { horizontal: } y = 3 \text {; vertical } x = - 1\)
• D) \(\text { horizontal: } y = - 3 \text {; vertical } x = - 1\)
• E) \(\text { horizontal: } y = 3 \text {; vertical } x = 1\)

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Definitions:

Long Distance

Refers to something that is located far away or involves a great amount of space between two points or locations.

Steep Slopes

Geographic areas where the land surface angles sharply, making it prone to erosion, landslides, and difficult for certain types of vegetation to root.

Fine-Grained Sediment

Sediments composed of particles that are too small to be seen without magnification, leading to a smooth texture.

Lagoon

A shallow part of the sea between the shoreline and a protecting feature, such as a reef or barrier island, farther out to sea.