Functions

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. In other words, a function assigns exactly one output value for each input value.

Function Notation

Functions are often denoted using function notation, which typically takes the form f(x), where f is the name of the function and x is the input value. The function f then produces the output value associated with the input x.

Domain and Range

The domain of a function is the set of all possible input values for the function. The range of a function is the set of all possible output values for the function.

Vertical Line Test

The vertical line test is a way to determine if a relation is a function. If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. If every vertical line intersects the graph at most once, then the relation is a function.

Types of Functions

There are many types of functions, such as linear functions, quadratic functions, exponential functions, trigonometric functions, and more. Each type of function has its own unique properties and characteristics.

Study Guide

Understand function notation and how to evaluate functions for specific input values.
Be able to identify the domain and range of a given function.
Practice using the vertical line test to determine if a relation is a function.
Study the properties and graphs of different types of functions, such as linear, quadratic, and exponential functions.
Work on problems involving composition of functions and function transformations.
Review how to solve equations involving functions, such as finding the inverse of a function.

By mastering these concepts and skills, you will have a solid understanding of functions and be well-prepared for any related assessments or exams.

◂Math Worksheets and Study Guides Eighth Grade. Functions

The resources above cover the following skills:

Grade 8 Curriculum Focal Points (NCTM)

Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Connections to the Grade 8 Focal Points (NCTM)

Algebra: Students encounter some nonlinear functions (such as the inverse proportions that they studied in grade 7 as well as basic quadratic and exponential functions) whose rates of change contrast with the constant rate of change of linear functions. They view arithmetic sequences, including those arising from patterns or problems, as linear functions whose inputs are counting numbers. They apply ideas about linear functions to solve problems involving rates such as motion at a constant speed.

Functions

Function Notation

Domain and Range

Vertical Line Test

Types of Functions

Study Guide

[Functions] Related Worksheets and Study Guides:

◂Math Worksheets and Study Guides Eighth Grade. Functions

The resources above cover the following skills: