Mathematics: Which statement describes whether the function is continuous at x = 2? O The function is continuous at x = 2 because f(2) exists. O The function is continuous at x = 2 because lim f(x) exists. X-2 The function is not continuous at x = 2 because f(2) does not exist. The function is not continuous at x = 2 because lim f(x) does not equal f(2). X-2

12,456 plus 2,667= 15,123lbs...

Which statement describes whether the function is

catherinesquitieri

13.06.2021

(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.

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