# Continuity of Functions: A Hop, Skip, and a Jump Quiz

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**Continuity of Functions**- Consider the following statements:

I. *f*(*c*) is defined

II. exists

III.

We say "*f* is continuous at *c*" if which of the following statements hold?

*f*graphed below?

*f*is discontinuous at

*x*= 1 because

*f*(1) does not exist.

*f*is discontinuous at

*x*= 1 because does not exist.

*f*is discontinuous at

*x*= 1 because

*f*is continuous at

*x*= 1.

Identify all points at which *f* is discontinuous.

*x*= 0,

*x*= 1

*x*= 1,

*x*= 2

*x*= 0,

*x*= 2

*x*= 0,

*x*= 1,

*x*= 2

*f*is discontinuous.

*x*= 1,

*x*= -2

*x*= 1,

*x*= 3

*x*= -2,

*x*= 3

*x*= 1,

*x*= -2,

*x*= 3

*f*continuous?

*f*discontinuous?

On which of the following intervals is *f* continuous?

On which of the following intervals is *f*(*x*) continuous?

*f*(

*x*) =

*x*+ 1 and

*g*(

*x*) =

*x*– 1. Which of the following statements is false?

*x*= 1.

*x*= -1.

*f*+

*g*is continuous at

*x*= 1.

*x*= 1.

*f*(

*x*) =

*e*

^{x}

*g*(

*x*) = sin(

*x*)

*h*(

*x*) = tan(

*x*)

*m*(

*x*) =

*x*

^{2}– 2

*x*+ 3