For which value of k is the function f(x) = kx + 2 continuous at x = 3? (2023)

For which value of k is the function f(x) = kx + 2 continuous at x = 3? (2023)

Step 1: Understand what it means for a function to be continuous at a point. A function is continuous at a point if you can draw it without lifting your pencil.
Step 2: Identify the function given in the question, which is f(x) = kx + 2.
Step 3: Recognize that f(x) = kx + 2 is a linear function. Linear functions are straight lines.
Step 4: Know that linear functions are continuous everywhere, including at x = 3.
Step 5: Conclude that the value of k does not affect the continuity of the function at x = 3.

Continuity of Functions – Understanding that linear functions are continuous everywhere, including at specific points.