Sketch the Graph of the Rational Function $y = \frac { 1 } { ( x + 1 ) ^ { 2 } }$

question 5

Multiple Choice

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { 1 } { ( x + 1 ) ^ { 2 } }$

• A) no x-intercepts; y-intercept: 1; no vertical asymptotes; horizontal asymptote: y = 0;
• B) no x-intercepts; y-intercept: 1; vertical asymptote: x = 1; horizontal asymptote: y = 0;
• C) no x-intercepts; y-intercept: 1; vertical asymptote: x = - 1; horizontal asymptote: y = 0;
• D) no x-intercepts; y-intercept: -1; vertical asymptote: x = 1; horizontal asymptote: y = 0;
• E) no x-intercepts; y-intercept: -1; no vertical asymptotes; horizontal asymptote: y = 0;

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Definitions:

Optimal Point

The most favorable condition or level for growth, yield, or efficiency.

Motivation

The psychological processes that arouse and direct goal-directed behavior, stemming from internal or external factors.

Intrinsic Motivation

refers to the internal drive to engage in an activity for its own sake, deriving satisfaction and fulfillment from the activity itself rather than from external rewards or pressures.

Nature

The influence of our inherited characteristics on our personality, physical growth, intellectual growth, and social interactions.