# Properties of Functions Assignment

### Krishnasai, Claire, Sai, and Daniel

## 3 things about functions

- A function relates an input to an output.
- A function can never have the same x-value in the set.
- 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)

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

## 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.