Finding Graphs of Functions in Nature

Go find functions in nature, and photograph them!

Studying Graphs of Functions?

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|

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