For the Following Rational Function, Identify the Coordinates of All $$f ( x ) = \frac { x ^ { 2 } - 16 } { x - 4 }$$

question 146

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.
- $$f ( x ) = \frac { x ^ { 2 } - 16 } { x - 4 }$$

• A) removable discontinuity at \(( - 4 , - 8 )\); no \(x\)-intercepts, \(y\)-intercept: \(\left( 0 , - \frac { 1 } { 16 } \right)\) asymptotes: \(y = 0\) and \(x = 4\)
• B) removable discontinuity at \(( 4,8 )\); x-intercept: \(( - 4,0 )\), y-intercept: \(( 0,4 )\); no asymptotes
• C) removable discontinuity at \(( 4,8 )\); no \(x\)-intercepts, \(y\)-intercept: \(\left( 0 , \frac { 1 } { 16 } \right)\) asymptotes: \(\mathrm { y } = 0\) and \(\mathrm { x } = 4\)
• D) removable discontinuity at \(( - 4 , - 8 )\); no \(x\)-intercept: \(( 4,0 )\), y-intercept: \(( 0 , - 4 )\); asymptotes: \(\mathrm { y } = 0\) and \(\mathrm { x } = 4\) no asymptotes

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