Final answer:
To find the value of the constant k that makes the function g(x) continuous, set the left-hand and right-hand limits equal to each other and solve for k.
Step-by-step explanation:
In order for a function to be continuous, it should have the same value for the left-hand and right-hand limits as it approaches a point. To find the value of the constant k that makes the function g(x) continuous, you need to set the left-hand and right-hand limits equal to each other and solve for k. For example, if you have the function g(x) = kx + 2 and you want it to be continuous at x = 3, you would set the left-hand limit g(3-) equal to the right-hand limit g(3+) and solve for k.
For example:
g(3-) = (3k + 2) = g(3+) = (3k + 2). By setting these two equations equal to each other, you can solve for k:
3k + 2 = 3k + 2, k = 0.