True or false: combining functions

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   The difference of two continuous functions is continuous.

2. Statement is true

   Yes

   Statement

   The product of two continuous functions is continuous.

3. Statement is true

   No

   Statement

   A quotient is continuous even where its denominator is zero.

4. Statement is true

   Yes

   Statement

   The chain rule handles composites of functions.

5. Statement is true

   Yes

   Statement

   Continuity is defined pointwise, then extended to the domain.

Explanation