Function Notation: Explanation and Study Guide

What is a Function?

A function is a relationship or rule that assigns each input (or value from the domain) to exactly one output (or value in the range). In other words, for each input, there is only one output. Functions are commonly denoted by the symbol "f".

Function Notation

Function notation is a way to represent functions using symbols and variables. It is commonly used to define, evaluate, and manipulate functions. Function notation typically involves the use of the function name followed by parentheses containing the input value. The general form of function notation is f(x), where f is the function name and x is the input value.

Using Function Notation

When using function notation, the input value (or independent variable) is substituted into the function to find the corresponding output value (or dependent variable). This is done by replacing x with the specific input value inside the parentheses.

Example:

Given the function f(x) = 2x + 3, to find the value of f(4), we substitute 4 for x in the function:
f(4) = 2*4 + 3 = 8 + 3 = 11
So, f(4) = 11.

Study Guide

When studying function notation, it's important to understand the following key concepts:

Understanding the meaning of function notation and its purpose in representing functions.
Practicing substitution of input values into functions using function notation to find output values.
Recognizing the difference between the function name and the input variable in function notation.
Applying function notation in various mathematical problems and real-world scenarios.
Understanding the relationship between the domain, range, input, and output of a function within the context of function notation.

Summary

Function notation is a powerful tool for representing and working with functions. By using symbolic notation, functions can be defined, evaluated, and manipulated more efficiently. Understanding function notation is essential for mastering the concept of functions in mathematics.

◂Math Worksheets and Study Guides Eighth Grade. Perimeter and area

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.