Function Notation Study Guide

What is a Function?

A function is a relationship or rule that assigns to each input value exactly one output value. In other words, it pairs each input with exactly one output.

Function Notation

Function notation is a way of representing a function. It uses a special notation to show the input and output of a function. The most common form of function notation is f(x), where f is the name of the function and x is the input value.

How to Use Function Notation

When using function notation, you replace the variable in the function with the input value given. For example, if you have a function f(x) = 2x + 3, and you want to find the output for an input of 5, you would substitute 5 in place of x, like this: f(5) = 2(5) + 3 = 13. So, when you see f(5), it means you're finding the output of the function when the input is 5.

Practice Questions

1. Find g(3) if g(x) = 4x - 2.
2. Given h(x) = 3x^2 + 2x - 5, evaluate h(2).
3. If p(x) = 5x^3 - 2x^2 + 7, what is p(-1)?

Answers

1. g(3) = 4(3) - 2 = 12 - 2 = 10
2. h(2) = 3(2)^2 + 2(2) - 5 = 3(4) + 4 - 5 = 12 + 4 - 5 = 11
3. p(-1) = 5(-1)^3 - 2(-1)^2 + 7 = 5(-1) - 2(1) + 7 = -5 - 2 + 7 = 0