which of the following functions is continuous at x = 5? (5 points)
f of x equals the quantity x squared minus twenty five divided by the quantity x plus five
f of x equals the quotient of the quantity x squared minus 25 and the quantity x minus 5 for x not equal to 5 and equals 20 for x equals 5
f of x equals the quotient of the quantity x squared minus 25 and the quantity x minus 5 for x not equal to 5 and equals 0 for x equals 5
all are continuous at x = 5

Step-by-step explanation:

Given:

We need to check the continuity of the functions at .

Option 1:

Plug in 5 for 'x' and check the value of .

So, the function is defined at and around and equal to 0. So, it is continuous at .

Option 2:

The given function is defined at and is equal to 20 but it has a different value around 5.

So, the function has a value of 10 around and equal to 20 at  . So, it is not continuous at  .

Option 3:

The given function is defined at and is equal to 0 but it has a different value around 5.

So, the function has a value of 10 around and equal to 0 at  . So, it is not continuous at  .