Determine what, if any, value to assign to $f ( a )$ to make f continuous at $x = a$ . $f ( x ) = \frac { x ^ { 2 } - 6 x + 8 } { x - 4 }$ ; $a = 4$
A) $f ( 4 ) = 6$
B) $f ( 4 ) = - 6$
C) $f ( 4 ) = 2$
D) $f ( 4 ) = - 4$
E) No value of $f ( 4 )$ will make it continuous at 4.

Question

Determine what, if any, value to assign to $f ( a )$ to make f continuous at $x = a$ .   $f ( x ) = \frac { x ^ { 2 } - 6 x + 8 } { x - 4 }$ ; $a = 4$  
A) $f ( 4 ) = 6$
B) $f ( 4 ) = - 6$
C) $f ( 4 ) = 2$
D) $f ( 4 ) = - 4$
E) No value of $f ( 4 )$ will make it continuous at 4.

Quizplus · Accepted Answer

The function can be simplified to $f(x) = x - 2$ for $x \neq 4$. The limit as $x$ approaches 4 is 2, so assigning $f(4) = 2$ makes the function continuous at $x = 4$.

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