For the Following Rational Function, Identify the Coordinates of All $$f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }$$

question 23

Multiple Choice

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes.
- $$f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }$$

• A) no removable discontinuities; no \(\mathrm { x }\)-intercept, no \(\mathrm { y }\)-intercept asymptotes \(x = 3 , x = 4 , y = 0\)
• B) no removable discontinuities; no \(\mathrm { x }\)-intercept, no \(\mathrm { y ; no \(x\)-intercept, no \(y\)-intercept; asymptotes \(x = - 3 , x = - 4 , y = 0\)
• C) removable discontinuity at \(( - 4 , - 1 )\); no \(x\)-intercept, \(y\)-intercept: \(\left( 0 , \frac { 1 } { 3 } \right)\); asymptotes \(x = - 3 , y = 0\)
• D) removable discontinuity at \(( 4,1 )\); no \(x\)-intercept, \(y\)-intercept: \(\left( 0 , - \frac { 1 } { 3 } \right)\) asymptotes \(x = 3 , y = 0\)

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Definitions:

Capacity

In legal terms, the ability of an individual or entity to enter into a contract, often requiring them to be of legal age and sound mind.

Substantive Unconscionability

A principle in contract law where a contract or a specific term is so unfairly one-sided that it is deemed unconscionable and unenforceable.

Procedural Unconscionability

Refers to a situation in contract law where the manner in which a contract was formed is unfair or oppressive, often due to unequal bargaining power or lack of choice.

Adhesion Conscionability

Adhesion conscionability examines whether a contract, typically a "take-it-or-leave-it" deal presented by the stronger party to the weaker, is so one-sided that it is unfair to the weaker party and therefore unenforceable.