What activities can my algebra class do to help understand different types of functions?

I’m helping with a college-level algebra class, and our class is set up around functions. We use them to introduce different algebraic concepts. For example, this week we’re looking at linear functions, which required us to get a better understanding of graphs and tables. Next week we’re looking at quadratic functions, which will require us to factor (i.e. where does the graph intersect the x-axis?). Get the picture?

I want them to be able to understand how the functions work, though. For linear functions, we had a “race” where everyone had a difference pace (represented by slope), and some people began early or started later (y-intercept), etc.

>>>What kind of activity can we do so that they understand what quadratic functions are like? Exponential? Inverse? Square root? Logarithmic? Absolute Value?

Humorous answers welcome. They can spark ideas.