Limits-Based Continuity

Based upon the three-part definition of continuity, is the function continuous at x = 0?

• Yes!

• Nope. There's a removable discontinuity, silly.

• Nope. Infinite discontinuity, fool.

• Nope. Jump discontinuity, pal.

Based upon the three-part definition of continuity, is the function continuous at x = 2?

• Yes!

• Nope. Removable continuity, chump.

• Nope. Infinite discontinuity, fool.

• Nope. Jump continuity, jerk.

Based upon the three-part definition of continuity, what must a equal in order for the function to be continuous?

• a = 0

• a = 4

• a = 1

• There is no value of a for which this function is continuous.

Is the function continuous at x = -2?

• Yup.

• Nope. Infinite discontinuity, friend.
  

• Nope. Jump discontinuity, bucko.

• Nope. Removable discontinuity, guy.

Is the function continuous at x = 6?

• Yep.

• Nope. Jump discontinuity, pal.

• Nope. Infinite discontinuity, noob.

• Nope. Removable discontinuity, dog.

Is the function continuous at x = -6?

• Yes!

• No! Jump discontinuity, yo!

• No! Infinite discontinuity, you amateur!

• No! Removable discontinuity, you rapscallion!

Is the function continuous at x = 1?

• Yerp.

• No? Like, this is obviously an infinite discontinuity?

• Uh, no? Only an absolute fool would fail to recognize this as a jump discontinuity?

• No...? This is a removable discontinuity...?

Identify all points of discontinuity in the function.

• x = -4, x = 2

• x = -4, x = -1, x = 2

• x = -4, x = 2, x = 4

• None. This is a thoroughly continuous function.