Let $f ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }$ . Which of the following is true?

A)ƒ is defined at -2.
B)ƒ is defined at 2.
C)ƒ has a removable discontinuity at -2.
D)ƒ has a removable discontinuity at 2.
E)ƒ is continuous at -2.

Question

Let $f ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }$ . Which of the following is true?

A)ƒ is defined at -2.
B)ƒ is defined at 2.
C)ƒ has a removable discontinuity at -2.
D)ƒ has a removable discontinuity at 2.
E)ƒ is continuous at -2.

Quizplus · Accepted Answer

The function $f(x)$ has a removable discontinuity at $x = 2$ because both the numerator and the denominator become zero at $x = 2$, indicating a common factor that can be canceled.

Let f(x)=x3−8x2−4f ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }f(x)=x2−4x3−8​

Let $f ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } - 4 }$