Determine all values of x at which the function is discontinuous.
A) 0, 4
B) 0, -4
C) -5
D) 5
E) -4

Question

Determine all values of x at which the function is discontinuous. ​  ​
A) 0, 4 
B) 0, -4 
C) -5 
D) 5 
E) -4

Quizplus · Accepted Answer

The function is defined as f(x) = $\dfrac{x^2 - 16}{x - 4}$. For x ≠ 4, f(x) simplifies to f(x) = (x + 4) and as the function is a polynomial function, it is continuous everywhere except at x = 4. However, at x = 4, the denominator becomes 0, leading to an undefined function. Therefore, the function is discontinuous at x = 4. Additionally, the function is undefined at x = 0 as well because it results in division by 0. Therefore, the function is discontinuous at x = 0 and x = 4.

Determine All Values of X at Which the Function Is