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:

Systematic Desensitization

A behavioral therapy method used to reduce phobias, anxiety, and fears through gradual exposure to the feared object or situation.

Relaxation Techniques

Various practices used to reduce stress and anxiety, promoting a state of calm and physical relaxation.

Flooding

A psychological treatment method where individuals are exposed to their fears or phobias in a controlled and safe environment, with the aim of extinguishing the fear response.

Paradoxical Intent

A therapeutic technique in which a person tries to bring about a feared outcome, often resulting in the reduction of the fear’s intensity.