# Relation vs. Function

Have you ever wondered about functions?  What makes a function a function?  Why is it different than a relation? Functions hold a special place in mathematics, in that they describe the dependencies between values, inputs and outputs, ingredients and baking.  What ingredients we put into a cake mix depends on the type of cake we desire.  Similarly, a function can be describe (loosely) as a recipe, what you put into the recipe determines what your result will be.

To gain a bit better understanding of how functions are determined and defined, watch the following three videos.  Take notes as you watch, particularly about ideas or concepts that might be new or you still have questions about. After each video return to this page using the back arrow.

How do you figure out if a relation is a function? | Virtual Nerd

What’s a Function? | Virtual Nerd

Recognizing functions from table (video) | Khan Academy

(If you are really interested, notice along the left menu bar there are more videos about functions you can can watch!)

Evaluating a function

Try the following:  Find $$f(2)$$, $$f(-2)$$, $$f(a)$$ when $$f(x)=x^2+3x-1$$

Once you are done watching the videos and trying to evaluate the function, go on to the next part of the lesson.

Did you find the following values for the function?

9, $$-3$$, $$a^2+3a-1$$