Function Definition Math: Grade 8 Simple Explanation
๐ What is a Function?
Imagine a function like a vending machine. You put something in (an input), and it gives you something else out (an output). In math, we usually call the input "x" and the output "y". A function is a special rule that tells you exactly how to get from "x" to "y".
โ Function Notation
We write functions using a special notation. The most common way is:
$f(x)$
This is read as "f of x". It means "apply the function 'f' to the input 'x'". For example, if we have the function $f(x) = x + 2$, this means whatever number you put in for 'x', you add 2 to it to get the output.
โ๏ธ Example Time!
Let's say our function is $f(x) = 3x - 1$.
- ๐ข If we put in $x = 2$, then $f(2) = 3(2) - 1 = 6 - 1 = 5$. So, the output is 5.
- โ If we put in $x = 0$, then $f(0) = 3(0) - 1 = 0 - 1 = -1$. So, the output is -1.
- โ If we put in $x = -1$, then $f(-1) = 3(-1) - 1 = -3 - 1 = -4$. So, the output is -4.
โ๏ธ How to Tell if Something is a Function
The most important rule: for every input (x), there can only be one output (y). Think back to the vending machineโyou wouldn't expect to put in a dollar and sometimes get a soda and sometimes get chips, right?
๐ Using a Table
Sometimes, we see functions represented in a table. Let's look at an example:
| x (Input) |
y (Output) |
| 1 |
4 |
| 2 |
5 |
| 3 |
6 |
This table shows a function because each 'x' value has only one corresponding 'y' value. A simple function that defines this is $f(x) = x + 3$.
๐ Using a Graph
You can also see functions on a graph. A handy trick to check if a graph represents a function is the vertical line test. If you can draw a vertical line anywhere on the graph and it only crosses the line once, then it's a function. If it crosses more than once, it's NOT a function.
โ๏ธ Practice Quiz
Let's test your knowledge! Which of the following represents a function?
- โ Given $f(x) = 2x + 5$, what is $f(3)$?
- โ Is the following a function? x = 1, y = 2; x = 2, y = 4; x = 3, y = 6; x = 1, y = 8
- โ If $g(x) = x^2 - 3$, what is $g(-2)$?
- โ A vending machine has items priced based on the number you input. Is this a function? Why or why not?
- ๐ก What does $f(x)$ mean in function notation?
- ๐ Explain the vertical line test and how it helps determine if a graph is a function.
- ๐ If $h(x) = 5$, what is $h(10)$? What kind of function is this?
