1.10: Exploring Types of Discontinuities

Which graph is an example of removeable discontinuity?

• 
• 
• 
• 

The graph above has what type of discontinuity?

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• No discontinuity

The graph above has what type of discontinuity at x = 2.

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• Oscillating Discontinuity

The graph above has what type of discontinuity at x = -1.

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• Oscillating Discontinuity

The graph above has what type of discontinuity at x = -3.

• Removable discontinuity

• Jump discontinuity

• Infinite discontinuity

• Oscillating Discontinuity

The function $f$ displayed above has a removable discontinuity at 

• x = 0

• x = 1

• x = 2

• x = 3

• none of these

The function $f$ displayed above has a jump discontinuity at

• x = -1

• x = 1

• x = 2

• x = 3

• none of these

• Removable discontinuity at x = 3

• Jump discontinuity at x = 3

• Infinite discontinuity at x = 3

• Continuous at x = 3

Given a function,  $f\left(x\right)$  , if 
 $\lim_{x\rightarrow2}\ f\left(x\right)=\ 4\$ and  $f\left(2\right)=-3$ , which of the following is true?

Which type of discontinuity is described?    

• Removable discontinuity at x = 2

• Jump discontinuity at x = 4

• Infinite discontinuity at x = 4

• Continuous at x = 4

Given a function,  $f\left(x\right)$  , if 
 $\lim_{x\rightarrow4^-}\ f\left(x\right)=\ 3,\ \lim_{x\rightarrow4^+}\ f\left(x\right)=\ -1\$ and  $f\left(4\right)=9$ , which of the following is true?

Which type of discontinuity is described?    

• Removable discontinuity at x = 4

• Jump discontinuity at x = 4

• Infinite discontinuity at x = 4

• Continuous at x = 4