Use a graph of f or some other method to determine what, if any, value to assign to $f ( a )$ to make f continuous at $x = a$ . $f ( x ) = \frac { x ^ { 2 } - 2 x } { x + 5 }$ ; $a = - 5$
A)15
B) 37
C) 35
D) 12
E) No value of $f ( - 5 )$ will make it continuous at -5.

Question

Use a graph of f or some other method to determine what, if any, value to assign to $f ( a )$ to make f continuous at $x = a$ .   $f ( x ) = \frac { x ^ { 2 } - 2 x } { x + 5 }$ ; $a = - 5$  
A)15
B) 37
C) 35
D) 12
E) No value of $f ( - 5 )$ will make it continuous at -5.

Quizplus · Accepted Answer

The function $f(x) = \frac{x^2 - 2x}{x + 5}$ simplifies to $f(x) = \frac{x(x - 2)}{x + 5}$. At $x = -5$, the denominator becomes 0, which makes the function undefined at this point. Therefore, no value of $f(-5)$ can make it continuous at $x = -5$, as continuity requires the function to be defined at the point in question.

Use a Graph of F or Some Other Method to Determine