# How to Solve Function Notation

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

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

### Download Function Notation Worksheet

1. $$\color{blue}{13}$$
2. $$\color{blue}{15}$$
3. $$\color{blue}{0}$$
4. $$\color{blue}{-20}$$
5. $$\color{blue}{16}$$
6. $$\color{blue}{57}$$

36% OFF

X

## How Does It Work?

### 1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

### 2. Add to Cart

Add the eBook to your cart.

### 3. Checkout

Complete the quick and easy checkout process.

### 4. Download

Immediately receive the download link and get the eBook in PDF format.

## Why Buy eBook From Effortlessmath?

Save up to 70% compared to print

Instantly download and access your eBook

Help save the environment

Lifetime access to your eBook

Over 2,000 Test Prep titles available

Over 80,000 happy customers

Over 10,000 reviews with an average rating of 4.5 out of 5

24/7 support

Anytime, Anywhere Access