Domain and Range

When dealing with functions in math, it's important to understand the concepts of domain and range. The domain of a function refers to the set of all possible input values (x-values) for the function, while the range refers to the set of all possible output values (y-values) for the function.

Domain

The domain of a function is the set of all possible input values that the function can accept. When looking at the graph of a function, the domain is the set of all x-values that correspond to points on the graph. In other words, it is the set of all possible values that x can take on in the function.

Example:

Consider the function f(x) = x^2. In this case, the domain is all real numbers, since you can plug in any real number for x and the function will produce a valid output.

Range

The range of a function is the set of all possible output values that the function can produce. When looking at the graph of a function, the range is the set of all y-values that correspond to points on the graph. In other words, it is the set of all possible values that f(x) can take on for the given domain.

Example:

For the function f(x) = x^2, the range is all non-negative real numbers, since the function will only produce non-negative outputs for any input value of x.

Study Guide

To understand and work with domain and range, here are some key points to remember:

Domain refers to the set of all possible input values for a function.
Range refers to the set of all possible output values for a function.
When looking at the graph of a function, the domain is the set of all x-values and the range is the set of all y-values.
Some common restrictions on domain include division by zero and taking the square root of a negative number.
When working with functions algebraically, pay attention to any restrictions on the domain and the resulting range of the function.

◂Math Worksheets and Study Guides Sixth Grade. Area

The resources above cover the following skills:

Geometry (NCTM)

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.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.