For the Following Rational Function, Identify the Coordinates of All $$f ( x ) = \frac { \left( x ^ { 2 } - 9 \right) ( x + 5 ) } { \left( x ^ { 2 } - 25 \right) ( x + 3 ) }$$

question 151

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.
- $$f ( x ) = \frac { \left( x ^ { 2 } - 9 \right) ( x + 5 ) } { \left( x ^ { 2 } - 25 \right) ( x + 3 ) }$$

• A) removable discontinuity at \(( - 3,0 )\); \(x\)-intercept: \(( - 3,0 ) , y\)-intercept: \(\left( 0 , \frac { 3 } { 5 } \right)\) asymptotes: \(x = - 5 , y = 1\)
• B) removable discontinuity at \(( - 3 , - 3 )\); \(x\)-intercept: \(( 3,0 ) , y\)-intercept: \(\left( 0 , - \frac { 3 } { 5 } \right) ;\) asymptotes: \(x = - 5 , y = 1\)
• C) removable discontinuities: \(\left( - 5 , \frac { 4 } { 5 } \right) , \left( - 3 , \frac { 3 } { 4 } \right)\) \(x\)-intercept: \(( 3,0 ) , y\)-intercept: \(\left( 0 , \frac { 3 } { 5 } \right)\) asymptotes: \(x = 5 , y = 1\)
• D) removable discontinuities: \(\left( - 5 , \frac { 1 } { 5 } \right) , ( - 3,0 )\); \(x\)-intercept: \(( - 3,0 ) , y\)-intercept: \(\left( 0 , - \frac { 3 } { 5 } \right)\) asymptotes: \(x = 5 , y = 1\)

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