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Activity2.12Discontinuous Formulas

Discontinuities are a little more challenging to identify when working with formulas than when working with graphs. One reason for the added difficulty is that when working with a function formula you have to dig into your memory bank and retrieve fundamental properties about certain types of functions.

Subsection2.12.1Exercises

1

What would cause a discontinuity on a rational function (a polynomial divided by another polynomial)?

2

If \(y\) is a function of \(u\), defined by \(y=\fe{\ln}{u}\), what is always true about the argument of the function, \(u\), over intervals where the function is continuous?

3

Name three values of \(\theta\) where the function \(\fe{\tan}{\theta}\) is discontinuous.

4

What is the domain of the function \(k\), where \(\fe{k}{t}=\sqrt{t-4}\)?

5

What is the domain of the function \(g\), where \(\fe{g}{t}=\sqrt[3]{t-4}\)?