Use the Graph to Determine the Limit Visually (If It $g ( x ) = \frac { x ^ { 3 } - x } { x - 1 }$

question 247

Multiple Choice

Use the graph to determine the limit visually (if it exists) .Then identify another function g₂(x) that agrees with the given function at all but one point.
$g ( x ) = \frac { x ^ { 3 } - x } { x - 1 }$ $$\lim _ { x \rightarrow - 1 } g ( x ) = ?$$

• A) \(g _ { 2 } ( x ) = x ( x + 1 )\) \(\lim _ { x \rightarrow - 1 } g ( x ) = 0\)
• B) \(g _ { 2 } ( x ) = 3 x ^ { 2 } + 1\) \(\lim _ { x \rightarrow - 1 } g ( x ) = 4\)
• C) \(g _ { 2 } ( x ) = 3 x ^ { 2 } - 1\) \(\lim _ { x \rightarrow - 1 } g ( x ) = 2\)
• D) \(g _ { 2 } ( x ) = x ( x - 1 )\) \(\lim _ { x \rightarrow - 1 } g ( x ) = 2\)
• E) \(g _ { 2 } ( x ) = x ( x + 1 )\) \(\lim _ { x \rightarrow - 1 } g ( x ) = 4\)

---

Definitions:

Paradigm Shift

A fundamental change in the underlying assumptions or methodologies of a particular scientific discipline or wider social view.

Transference

The process wherein clients project feelings and attitudes from past relationships onto the therapist, often discussed in psychoanalytic and psychodynamic therapies.

Blank Screen Behavior

A psychoanalytic concept where the therapist maintains a neutral demeanor to encourage the patient to project their thoughts, feelings, and fantasies onto the therapist.

Impulse Control

The ability to resist or delay an impulsive action or response.