Question

For what value of k does the function h(x) = 2x + k become continuous on the interval [0, 5]?

a) k = 5
b) k = 0
c) k = 2.5
d) There is no value of k that makes h(x) continuous on [0, 5].

Answer 1

The function h(x) = 2x + k cannot be made continuous on the interval [0, 5].

Step-by-step explanation:

To determine the value of k that makes the function h(x) = 2x + k continuous on the interval [0, 5], we need to ensure that the function is continuous at the endpoints of the interval.

In this case, we have h(0) = 2(0) + k = k and h(5) = 2(5) + k = 10 + k.

To make the function continuous at the endpoints, the values of h(0) and h(5) should be equal. Therefore, we need to solve the equation k = 10 + k to find the value of k.

Simplifying the equation, we get 0 = 10, which is not true for any value of k. Therefore, the answer is d) There is no value of k that makes h(x) continuous on [0, 5].