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

question 187

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.
- $$f ( x ) = \frac { x } { x ^ { 2 } - 4 x }$$

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

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Definitions:

Construction

The process of building, erecting, or assembling structures, typically involving large-scale projects like buildings, roads, or bridges.

Reconstruction

The process of reassembling or reinterpreting something, often used in the context of remembering events differently from how they actually occurred.

Equipotentiality

The idea that any part of a particular functional area of the brain can perform its associated function, emphasizing brain plasticity.

Amnesia

A condition characterized by the loss of memories, such as facts, information, and experiences, which can be temporary or permanent.