Review Quiz in Basic Calculus

A function is considered continuous if:

• The graph has breaks or holes

• It can be drawn without lifting the pencil

• It is not defined for some values

• It has jumps between values

Which of the following is an example of a discontinuous function?

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What must be true for a function to be continuous at x=c?

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What is the left-hand limit of a function?

• The function value approaching from the right

• The function value approaching from the left

• The actual function value

• The average of all function values

Which type of discontinuity is removable?

• A function with a hole at a point

• A function with a jump between values

• A function that approaches infinity

• A function with no limits

If a function is continuous on an interval, then:

• It has a gap somewhere in the graph

• It can have a jump at one point

• It has no breaks, holes, or jumps

• It is always differentiable

The function f(x)=⌊x⌋ (greatest integer function) has what kind of discontinuity?

• Jump

• Removable

• Infinite

• None

What is the open interval notation for all real numbers except x=5?

• (−∞,5]∪[5,∞)

• (−∞,5)∪(5,∞)

• (−∞,5)

• (5,∞)

A function is not continuous at a point if:

• It has a removable discontinuity

• It has a jump discontinuity

• It has an infinite discontinuity

• All of the above

Which of the following is an example of an infinite discontinuity?

• f(x)=∣x∣

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