Text Formatting ⇒ multicols problem

[coachbennett1981]

I can't seem to figure out why the second \paragraph is included in the multicol directly below it. Does anyone know how to fix this?

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\documentclass[12pt]{exam}
\usepackage{geometry}                % See geometry.pdf to learn the layout options. There are lots.
\geometry{letterpaper}                   % ... or a4paper or a5paper or ... 
%\geometry{landscape}                % Activate for for rotated page geometry
%\usepackage[parfill]{parskip}    % Activate to begin paragraphs with an empty line rather than an indent
\usepackage{graphicx}
\usepackage{amssymb}
\usepackage{multicol}
\usepackage{amsmath}
\usepackage{pst-plot}
\usepackage{pstricks-add}
\addpoints
\DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `dirname #1`/`basename #1 .tif`.png}
\pagestyle{headandfoot}
\firstpageheader{Section 2.6}{Precalculus}{Rational Functions and Their Graphs}
\runningheader{Section 2.6}{Precalculus}{Rational Functions and Their Graphs}
\firstpagefooter{}{}{}
\begin{document}


\fbox{\begin{tabular}{p{6in}}


 
\end{tabular}}

\paragraph{Example 1} Find the domain of each rational function:
	\begin{multicols}{3}
		\begin{parts}
			\part $f(x)=\dfrac{x^2-25}{x-5}$
			\part $g(x)=\dfrac{x}{x^2-25}$
			\part $h(x)=\dfrac{x+5}{x^2+25}$
		\end{parts}
	\end{multicols}
		\vspace{1in}
\paragraph{Check Point 1}

		\begin{multicols}{3}{
			\begin{parts}
				\part $f(x)=\dfrac{5x}{x-4}$
				\part $g(x)=\dfrac{x+7}{x^2-49}$
				\part $h(x)=\dfrac{x+7}{x^2+4}$
			\end{parts}
			}
		\end{multicols}
		
\end{document}

[bev]

The problem is the way the \paragraph macro is implemented. It has zero vertical space (iirc), and so \muliticols is tricked. There are three solutions that I've found so far. The first is to put some text after the \paragraph arg:

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\paragraph{Check Point 1} Let's check some points!

the second is to forgo \paragraph altogether and do something like:

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{\parindent0pt \bfseries Check Point 1}

which looks exactly the same to me.

Lastly, make a macro that just takes up some vertical space, but it not visible:

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\newcommand{\blee}{\rule{1cm}{0pt}}
\paragraph{Check Point 1}\blee

Or, you could always fix the problem with the \paragraph macro, where ever it's defined in this case.

[coachbennett1981]

Thank you for your help. I actually added some text and got your first result and it worked. I liked your macro idea.

Nick