# Properties of Functions Assignment

## 3 things about functions

1. A function relates an input to an output.
2. A function can never have the same x-value in the set.
3. The function must work for every possible input value.

## Composition of functions

"Function Composition" is applying one function to the results of another.

• f(x) - g(x)
The result of f(x) is sent through g(x).

It is written like this: g(f(x)).

## Real life example #1 - Quadratic function

Definition: The highest power over the x variable (s) is 2.

If you kick a soccer ball up into the air, it will arc up and come down again following the path of a parabola. This is an example of a quadratic function.

## Real life example #2 - Linear function

Definition: The highest power over the x variable is 1.

You can rent an electricity generator for \$4.80 per hour plus \$100.00 for a full tank of petrol (Let y represent the cost of using the generator. Let x represent the hours.) The cost is \$4.80 per hour plus \$100.00 for a the petrol tank (y=100.00+4.80x). When graphed, this function creates a line thus making it an example of a linear function.

## Real life example #3 - Logarithmic function

Definition: Inverses of exponentials

• Exponential: y=a^x
• Logarithmic: y=log(x)

The example that corresponds to the graph is population growth. An initial number of bacteria presented in a culture is 10000. This number doubles every 30 minutes. This is an example of a logarithmic function.