Continuity on functions

Question

To two decimal places, find the value of k that will make the function f(x) continuous everywhere.

Options:

1. 22.00
2. -0.92
3. -1.76
4. None of these

Answer 1

5x+k for x ≤ -5 is a function on the range specified.

kx^2 – 3 for x > -5 is a function on the range specified.

The two partial functions become continuous when they have the same value for x -5:

That is, when    5x+k = kx^2 – 3

or,

      5(-5) + k = k(-5)(-5) – 3

       -25 + k = 25k – 3

       -22 = 24k

       k = -24/22

       k = -1.09091

To two decimal places, that is k = -1.09

     4. None of these

Answer 2

For the function to be continuous, the 2 expressions need to be equal when x = -5. So....just plug in -5 for x, set the expressions equal, and solve for k