EXERCISE #4: Secret Function
INDOOR GROUP
Required materials:
-small paper and a writing utensil
-larger surface with a corresponding writing utensil, used to write a mathematical function displayed to the whole group
How it works:
Who wants to be an INPUT?
Who wants to be an OUTPUT?
Example function: f(x) = 2x
The above mathematical expression may seem like gibberish to you, but don’t worry! We’ll work through it together, and you can see the Background section below if you need more detail.
The INPUT and OUTPUT participants decide on a secret mathematical function that can be expressed like the example you see above. In this expression, there must be at least one mathematical operation: addition, subtraction, division, multiplication. The INPUT and OUTPUT participants write down their secret function somewhere (hidden so no other group members can see it).
Once the I/O participants decide on a function, the rest of the group will take turns assigning an INPUT value (the value of ‘x‘) and getting the resulting OUTPUT value. Keep track of all your tested INPUT and resulting OUTPUT values in a chart, or table, that can be displayed to all group members. How many test values does it take for the group to figure out what secret mathematical function is being used?
REMEMBER:
The group should always test the same INPUT value more than once. If the resulting OUTPUT changes then you know something’s wrong and the group can shout,
“THAT’S NOT A FUNCTION!“
Example function: f(x) = 2x
Our example shows the number 2 being multiplied by the letter ‘x‘. When we write this function down, we don’t know what number x represents yet. We’ll substitute different INPUT number values into the spot that x holds. On the left side of the expression, we’ll show the value we’re substituting in for x. This is different from how we usually interpret braces in a mathematical expression. When we see braces beside ‘f‘ then we know we’re using them to represent the substitution of a value for x.
On the right side of the expression, we’ll eventually get the result of our INPUT value substituted for x. Lets return to our example, and substitute some values for x. We’ll use the ‘*‘ character to represent multiplication.
f(3) = 2*3
f(3) = 6
f(4) = 2*4
f(4) = 8
Group members attempting to guess the secret function could use the following chart (or table) to keep track of INPUT values and their resulting OUTPUT.
| f(x) | = | OUTPUT |
|---|---|---|
| f(3) | = | 6 |
| f(4) | = | 8 |
| f(5) | = | 10 |
Background:
The most important rule for a mathematical function is allowing only one corresponding OUTPUT value for a given INPUT value. If you’re wondering what kind of mathematical operations could result in multiple OUTPUT values for a single INPUT value, consider the square root operation. When you find the square root of a number, like 36, you discover there are two results, a negative and a positive root: -6 and +6. Each of these roots produces the same result when squared. Because two different results are obtained from the same INPUT value, a square root operation isn’t a function.
There’s a lot of further detail with regards to the collection of values representing INPUT and all corresponding OUTPUT values. If you’re looking to do further reading then you might want to checkout definitions for the ‘domain‘ and corresponding ‘range‘ of a function. You might also be interested in terms like the ‘graph‘ of a function, as well as ‘independent‘ and ‘dependent‘ variables.