Question

Is a square root function continuous at 0?

A) Yes, square root functions are continuous at 0.
B) No, square root functions have a jump discontinuity at 0.
C) Square root functions are only continuous at integers.
D) Square root functions are continuous everywhere except at 0.

Answer 1

Yes, square root functions are continuous at 0.

Step-by-step explanation:

A square root function is continuous at a point if the limit as x approaches that point exists and is finite. In the case of a square root function, it is continuous at 0. This is because as x approaches 0 from the right side, the square root of x approaches 0 as well. Similarly, as x approaches 0 from the left side, the square root of x approaches 0. Therefore, the limit of the function as x approaches 0 exists and is equal to 0, making the square root function continuous at 0.