Learn what the definition of function is and how to write a function using function notation and how to avaluate a function.

## Related Topics

- How to Add and Subtract Functions
- How to Multiply and Dividing Functions
- How to Solve Composition of Functions
- How to find Inverse of a Function

## Step by step guide to solve Function Notation and **Evaluation**

- Functions are mathematical operations that assign unique outputs to given inputs.
- Function notation is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation.
- The most popular function notation is \(f(x)\) which is read “\(f\) of \(x\)”. Any letter can be used to name a function. for example: \(g(x)\), \(h(x)\), etc.
- To evaluate a function, plug in the input (the given value or expression) for the function’s variable (place holder, \(x\) ).

### Function Notation – Example 1:

Evaluate. \(h(n)=n^2-2\)

Find \(h(4)\).

**Solution:**

Substitute \((4)\) for \(n\) and solve. \(h(n)=n^2-2→h(4)=(4)^2-2→h(4)=16-2→h(4)=14\)

### Function Notation – Example 2:

Evaluate. \(w(x)=4x-1\)

Find \(w(2)\).

**Solution:**

Substitute \((2)\) for \(x\) and solve. Then: \(w(x)=4x-1→w(2)=4(2)-1→w(2)=8-1→w(2)=7\)

### Function Notation – Example 3:

Evaluate. \(w(x)=3x+1\)

Find \(w(4)\).

**Solution:**

Substitute \(x\) with \(4\): Then: \(w(x)=3x+1→w(4)=3(4)+1→w(x)=12+1→w(x)=13\)

### Function Notation – Example 4:

Evaluate. \(h(n)=n^2-10\)

Find \(h(-2)\).

**Solution:**

Substitute \(n\) with \(-2\): \(h(n)=n^2-10→h(-2)=(-2)^2-10→h(-2)=4-10→h(-2)=-6\)

## Exercises for Solving Function Notation

### Evaluate each function.

- \(\color{blue}{w(x) = 3x + 1, find \ w(4)}\)
- \(\color{blue}{h(n) = n^2 – 10, find \ h(5)}\)
- \(\color{blue}{h(x) = x^3 + 8, find \ h(–2)}\)
- \(\color{blue}{h(n) = – 2n^2 – 6n, find \ h(2)}\)
- \(\color{blue}{g(n) = 3n^2 + 2n, find \ g(2)}\)
- \(\color{blue}{g(n) = 10n – 3, find \ g(6)}\)

### Download Function Notation Worksheet

- \(\color{blue}{13}\)
- \(\color{blue}{15}\)
- \(\color{blue}{0}\)
- \(\color{blue}{-20}\)
- \(\color{blue}{16}\)
- \(\color{blue}{57}\)