Question

Which statement describes whether the function is continuous at x = 2?

Answer 1

Answer: (b)

Step-by-step explanation:

Given

The function is given as

$f(x)=\dfrac{x^2-12x+20}{x-2}$

Solving the function

$f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10$

for $x=2$

$f(2)=2-10\\f(2)=-8$

The function is continuous at $x=2$ because $\lim_{x \to 2} f(x)$ exists.

If the limit exists at a point, then the function is continuous.