No, here is an example of a nonremovable discontinuity at \(x=c\) that is not a vertical asymptote. Click here for more information about nonremovable discontinuities.

A root of a function is just a fancy word for an x-intercept, i.e. it is where the graph crosses the x-axis. The term root is often used in engineering, especially electrical engineering. You can also call a root, a zero (since \(y=0\)).

Note that you can have multiple roots of a function since a graph can cross with the x-axis multiple times without failing the vertical line test, which is why we talk about A root and not THE root.

The word 'indeterminate' usually shows up when discussing limits and it means 'cannot be determined'. For example, when you take a limit and get the result \( 0/0 \), this is indeterminate, meaning the limit could be anything and cannot be determined with the given information.

Many times, you can determine the limit but in order to do so, you need to alter the function using algebra, trig or L'Hôpital's Rule to put it in a form so that is no longer indeterminate. You can find plenty of examples (practice problems) on the finite limits page, infinite limits page and L'Hôpital's Rule page.

You can find more information on 17Calculus: Indeterminate Forms (including a table listing most indeterminate forms you will see in calculus).