Q. 32 - Calculus

Question

Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.

f is continuous on [0, 2) but not on [0, 2].

Step-by-Step Solution

Answer

The function is not possible with given conditions.

Step 1. Given Information.

f is continuous in [0,2) and at the same time it is not continuous in [0,2].

Step 2. Function doesn't exist.

Now since it is given that function is continuous in [0,2) it means it doesn't have any break points in the interval from 0 to 2 inclusive 0 and exclusive 2. Now see the second information given it tells that function is not continuous in the interval 0 to 2 both 0 and 2 inclusive but it is contradicting the above condition because the inclusion or exclusion of just one point doesn't effect the continuity if that point is one of the extreme.

Therefore, the graph of the function is not possible.