Finding Graphs of Functions in Nature

Go find functions in nature, and photograph them!

Well, some graphs of functions appear a lot, so knowing their shapes gives you a much better shot at graphing them correctly and catching common errors.

What do you need?

Either a graphing calculator, or a printout of the graphs of functions
A park or nature trail with plenty of trees or backyard
A camera
A keen eye for natural (not human made) shapes

Here are a few examples:

y=mx+b graph

f(x) = mx + b

Reciprocal function

f(x) = 1/x

Square function

f(x) = x²

Square root function

f(x) = √x

Absolute Value function

f(x) = |x|

f(x) = e^x

And here are some example photos we took to give you an idea:

Graph of f(x) = mx + b

The graph of f(x) = mx+b is a straight line, thus you are looking for something in nature that resembles a straight line. For example:

stick straight line
TAKE A PIC!

Graph of f(x) = x² or -x²

The graph of f(x) = x² looks like a U, and -x² is like a ∩, thus you are looking for something that resembles a U or ∩. For example:

stick x squared
TAKE A PIC!

Graph of Square Root: f(x) = √x

The graph of f(x) = √x looks something like the lower case letter r, for example:

stick square root
TAKE A PIC!

Graph of Absolute Value: f(x) = |x|

The graph of f(x) = |x| looks some thing like the letter V, for example:

stick absolute function
TAKE A PIC!

See what other graphs you can find...

When done, compare your pics of nature to the graphs of functions and put together a presentation.

Activity courtesy of Hands On Math