Function notation is a way to show how one number affects another number using a special format.

A function, which we can call ( f ), takes an input, usually labeled ( x ), and gives us an output which we write as ( f(x) ). To find the output using function notation, just follow these simple steps:

1. Find the Function: Functions are usually named with letters like ( f ), ( g ), or ( h ). For example, if we have a function written as ( f(x) = 3x^2 + 2 ), you need to look for this equation.

2. Plug in the Input: Decide what number you want to use for ( x ). If you want to evaluate ( f ) when ( x ) is ( 4 ), you replace ( x ) in the function with ( 4 ): $f(4) = 3(4)^2 + 2$

3. Do the Math: Solve the equation step-by-step:

   • First, find ( (4)^2 = 16 ).
   • Then, multiply by ( 3 ): ( 3 \times 16 = 48 ).
   • Finally, add ( 2 ): ( 48 + 2 = 50 ). So, ( f(4) = 50 ).

4. Check for Limits: Always look for any rules about what numbers you can use. For example, if a function has a square root or division, make sure your input won't cause problems.

5. Different Types of Functions: There are many kinds of functions, like:

   • Linear: ( g(x) = 2x + 5 )
   • Quadratic: ( f(x) = x^2 - 4x + 4 )
   • Exponential: ( h(x) = 2^x )

6. Graphs of Functions: Drawing graphs of functions can help you see how they work. When you plot a function, you can often see important points, making it easier to understand.

In summary, to evaluate a function using function notation, first identify the function, then replace the input value, and simplify to find the output. Knowing these steps is important for understanding functions, especially in high school algebra!