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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