Graph the Rational Function $y = \frac { 2 - x ^ { 2 } } { 2 x + 4 }$

question 290

Multiple Choice

Graph the rational function. Include the graphs and equations of the asymptotes.
- $y = \frac { 2 - x ^ { 2 } } { 2 x + 4 }$

• A) asymptotes: \(x = - 4 , y = - \frac { 1 } { 8 } x + \frac { 1 } { 2 }\)
• B) asymptotes: \(x = - 2 , y = - \frac { 1 } { 2 } x + 1\)
• C) asymptotes: \(x = - 2 , y = - x + 2\)
• D) asymptotes: \(x = - 2 , y = - \frac { 1 } { 4 } x + \frac { 1 } { 2 }\)

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Definitions:

Hypothetical Syllogism

A logical argument consisting of two conditional statements and a conclusion that is logically inferred.

Modus Ponens

A form of deductive reasoning that asserts if a conditional statement "If P, then Q" is accepted as true and P is true, then Q must also be true.

Modus Tollens

A method of logical argument that infers the falsehood of a proposition from the impossibility of its consequence.

Hypothetical Syllogism

A form of reasoning where if the first condition holds, then the second condition must follow, leading to a conclusion if the initial hypothesis is true.