Finding Graphs of Functions in Nature

Go find functions in nature, and photograph them!

Studying Graphs of Functions? Well, there are certain graphs of functions that appear repeatedly and if you can learn to recognize their shapes you have 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|

natural exponential function
f(x) = ex

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:


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:


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:


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:


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