Determine the continuity of the function f(x) = 7x - 5 at the point x = 12.

The function must be defined at x = 12:

Since the function f(x) is defined as 7x - 5 for all real numbers, it is defined as x = 12.

The limit of the function as x approaches 12 must exist:

Taking the limit as x approaches 12, we have:

\$\lim_{x \to 2} { (7x - 5)} = 7(12) - 5 = 84 - 5 = 79 \$

The limit exists and is equal to 79.

The value of the function at x = 12 must be equal to the limit:

Evaluating the function at x = 12, we get:

\$ f(12) = 7(12) - 5 = 84 - 5 = 79 \$

Since the value of the function at x = 12 is equal to the limit, we can conclude that the function
f(x) = 7x - 5 is continuous at x = 12.

This choice Implies function’s discontinuity at x = 12, where it’s either undefined, the limit doesn’t exist or isn’t equal to the value

Discontinuous

This choice Indicates the function’s continuity at x = 12, meaning it’s defined, the limit exists and equals the value at x = 12

Continuous

The function is not continuous at x = 12; the value 64 does not satisfy the necessary conditions for continuity

64

The function lacks continuity at x = 12; the value 15 is inconsistent with the required conditions for continuity

15

Option

B

Can you summarize what you’ve understood in the above steps?