1.
What would cause a discontinuity on a rational function (a polynomial divided by another polynomial)?
Activity 2.12 Discontinuous 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.
Exercises Exercises
2.
If \(y\) is a function of \(u\text{,}\) defined by \(y = \fe{\ln}{u}\text{,}\) what is always true about the argument of the function, \(u\text{,}\) 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 \(k\text{,}\) where \(\fe{k}{t} = \sqrt{t-4}\text{?}\)
5.
What is the domain of the function \(g\text{,}\) where \(\fe{g}{t} = \sqrt[3]{t-4}\text{?}\)
