Continuity Practice

A polynomial function is continuous to all real numbers.

• TRUE

• FALSE

• f(a) is defined

• f(a) equals an integer

Answer explanation

As long as f(a) is defined the limit exists. The answer does not have to be an integer (whole number) for f(a) to be defined.

A function f(x) with a removeable discontinuity at a could have all the following characteristics EXCEPT:

• f(a) does not exist

• f(x) is a polynomial

Answer explanation

Polynomials are continuous for all x-values. A polynomial function will never have a discontinuity, removable or otherwise.

Choose the type of Discontinuity on the given graph

• Jump

• Infinite

• Removable

• Rational

What is the only requirement for a function f(x) to have a non-removable discontinuity?

• f(a) is undefined

• There is more than one requirement

Which of the following graphed functions has an infinite discontinuity?

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