# Continuity of Functions

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

Think you’ve got your head wrapped around

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

- Consider the following statements:

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

II. exists

III.

We say "*f* is continuous at *c*" if the following statements hold:

I

II

I, II

I, II, III

Q. Which of the statements is true about the function

*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.

Q. Let

Identify all points at which <em>f</em> is discontinuous.

*x*= 0,

*x*= 1

*x*= 1,

*x*= 2

*x*= 0,

*x*= 2

*x*= 0,

*x*= 1,

*x*= 2

Q. Identify all points at which

*f*is discontinuous.

*x*= 1,

*x*= -2

*x*= 1,

*x*= 3

*x*= -2,

*x*= 3

*x*= -1,

*x*= -2,

*x*= 3

Q. On which of the following intervals is

*f*continuous?

(-1,1)

(0,3)

(2,4)

(0,4)

Q. On which of the following intervals is

*g*discontinuous?

(-10,2)

(2,4)

(3,4)

(3,5)

Q. Let

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

(-2,0)

(1,5)

(4,6)

(-1,1)

Q. Let

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

(-1,1)

[0,1)

(-1,0]

[-1,1]

Q. Let

*f*(*x*) =*x*+ 1 and*g*(*x*) =*x*- 1. Which of the following statements is false?The function is continuous at

*x*= 1.The function is continuous at

*x*= -1.The function

*f*+*g*is continuous at*x*= 1.The function is continuous at

*x*= 1.Q. Which of the following functions is not continuous?

*f*(

*x*) = e

^{x}

*g*(

*x*) = sin(

*x*)

*h*(x) = tan(

*x*)

*m*(

*x*) =

*x*

^{2}-2

*x*+ 3