Functions Study Guide

What is a Function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

Function Notation

Functions are often denoted by a letter such as f, and the input variable is usually denoted by x. The output variable is denoted by f(x).

Domain and Range

The domain of a function is the set of all possible inputs, while the range is the set of all possible outputs.

Types of Functions

• Linear Functions: Functions that have a constant rate of change.
• Quadratic Functions: Functions that have a squared term in the equation.
• Exponential Functions: Functions where the variable is in the exponent.
• Trigonometric Functions: Functions such as sine, cosine, and tangent.

Function Operations

Functions can be added, subtracted, multiplied, or divided to create new functions. These operations can be represented using function notation.

Graphing Functions

Functions can be represented graphically, with the input values on the x-axis and the output values on the y-axis. The graph of a function can provide insights into its behavior and characteristics.

Study Tips:

• Practice identifying the domain and range of functions.
• Understand the different types of functions and their key features.
• Work on graphing functions and understanding the relationship between the graph and the function's behavior.
• Practice function operations to gain a better understanding of how functions can be combined and manipulated.

Remember, understanding functions is essential for higher-level math and science courses, so make sure to master this topic!

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