Question

Find the value(s) of k that makes the function continuous over the given interval. f(x) = kx, 0 ≤ x ≤ 3 f(x) = x², 3 < x ≤ 10 a) k = 0 b) k = 1 c) k = -1 d) Multiple values of k

Answer 1

The question asks to find the value of k that makes the function continuous over the interval.

We have the function f(x) which is equal to kx when x varies from 0 to 3 and x² when x varies from 3 to 10.

Since we are looking for the continuity of the function, the value of the function just to the right of 3 must be equal to the value of the function just to the left of 3. This provides us with the equation: k*3 = 3².

If we simplify this equation, we get: 3k = 9.

Solving for k, we divide 9 by 3 which gives us: k = 3.

Therefore, the value of k that makes the function continuous over the given interval is k = 3.

However, as per the given options (a - d), none include the correct answer k = 3. Hence, it's possible there may be an error in the question.