Activity 1: Continuity and Discontinuity

Consider the function f(x) = (x^2 - 4) / (x - 2). Is f(x) continuous at x = 2

• Yes, it is continuous.

• No, it is discontinuous because f(2) is undefined

• No, it is discontinuous because the limit as x approaches 2 does not exist

• It depends on the value of f(2)

Which of the following conditions must be met for a function f(x) to be continuous at x = a?

• f(a) is defined.

• lim (x→a) f(x) exists

• lim (x→a) f(x) = f(a)

• All of the above

Which of the following functions is continuous everywhere?

• f(x) = 1/x

• f(x) = tan(x)

• f(x) = |x|

• f(x) = 1/(x-1)

If a function f(x) is continuous on the closed interval [a, b], then which of the following is true?

• f(x) must be differentiable on (a, b)

• f(x) must be bounded on [a, b]

• f(x) has no discontinuities on [a, b]

• All of the above

This type of discontinuity occurs when the function redefine to make it continuous

• Removable Discontinuity

• Jump Discontinuity

• Infinite Discontinuity

• Discontinuity Functions

Which of the following indicates a removable discontinuity at x = a?

• The limit of f(x) as x approaches a does not exist

• f(a) is undefined, but the limit of f(x) as x approaches a exists

• The left-hand limit and right-hand limit at x = a are different

• f(a) is defined, but the limit of f(x) as x approaches a is infinite

The function f(x) = 1/x has what type of discontinuity at x = 0?

• Removable discontinuity.

• Jump discontinuity.

• Infinite discontinuity.

• No discontinuity.

A jump discontinuity occurs when:

• The function approaches infinity at a specific point.

• The function has a "hole" that can be filled.

• The left-hand limit and right-hand limit at a point are unequal but finite.

• The function is undefined at a point.

At which x-value is the function f(x) = (x+2)/(x-3) discontinuous?

• x = -2

• x = 0

• x = 3

• The function is continuous everywhere.

Which of the following is the example of continuity

• 
• 
• 
•