Final answer:
To determine values of the constants a and b for which a function f is continuous at x=2, we need to check if the limit of the function as x approaches 2 exists and is equal to the value of the function at x=2.
Step-by-step explanation:
To determine values of the constants a and b for which a function f is continuous at x=2, we need to check if the limit of the function as x approaches 2 exists and is equal to the value of the function at x=2.
Let's assume the function is defined as f(x) = ax + b. To be continuous at x = 2, both the limit as x approaches 2 and the value of the function at x = 2 should exist.
To find the limit, we evaluate the function as x approaches 2 from both sides: f(2-) and f(2+).
If f(2-) = f(2+) = f(2), then the function is continuous at x = 2.
For example, if we have f(x) = 3x + 4, the limit as x approaches 2 is f(2) = 3(2) + 4 = 10. Therefore, a = 3 and b = 4 would make the function continuous at x = 2.