# What is the relationship between range and domain

### Understand the relationship between domain and range, and use f(x) notation | LearnZillion

Identify the domain and range for relations described with words, symbols, tables, Relations and functions describe the interaction between linked variables. Yes. Oh, you were wondering what the relationship is? Well, we know that the domain of a function is the interval of x-values where the function. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the.

The range is the set of all second elements of ordered pairs y-coordinates.

### Domain and Range - MathBitsNotebook(A1 - CCSS Math)

Only the elements "used" by the relation or function constitute the range. Set Builder notation may be used to express domains and ranges. State the domain and range of the following relation: No, this relation is not a function. The eye colors are repeated.

**Relations & Functions**

State whether the relation is a function. While these listings appear in ascending order, ordering is not required. Do not, however, duplicate an element.

The x-value of "1" had two corresponding y-values 3 and State the domain and range for the elements matched in the diagram below. State whether the matches form a function. Note that the range is only the elements that were used.

It is the "possible" set from which output from the relation will fall. The co-domain is NOT necessarily the same as the range. There may be values in the co-domain that are never used. State the domain and range associated with the scatter plot shown below.

State whether the scatter plot is a function. No x-values repeat, and it passes the Vertical Line Test for functions.

Graphs that are composed of a series of dots, instead of a connected curve, are referred to as discrete graphs. A discrete domain is a set of input values that consist of only certain numbers in an interval. State the domain and range associated with the graph below. State whether this relation is a function. The arrows indicate that the graph continues off the visible grid, so assume that all real numbers are involved.

Graphs that are composed of a connected curve are referred to as continuous graphs. A continuous domain is a set of input values that consists of all numbers in an interval. State the appropriate domains for the functions shown below.

When functions are expressed as "rules" formulasbe sure to think about possible "problem" spots before stating the domain.

By putting all the inputs and all the outputs into separate groups, domain and range allows us to find and explore patterns in each type of variable.

Examples and Notation The domain and range of a function are often limited by the nature of the relationship.

### Relations, Functions, and Function Notation

For example, consider the function of time and height that occurs when you toss a ball into the air and catch it. Time is the input, height is the output. The domain is every value of time during the throw, and it runs from the instant the ball leaves your hand to the instant it returns. Time before you throw it and after you catch it are irrelevant, since the function only applies for the duration of the toss. The range is every height of the ball during the throw, and it includes all heights between your hand when you let the ball go and the highest point the ball reached before it began to fall back to you.

## Understand the relationship between domain and range, and use f(x) notation

If your hand was 3 feet above the ground when you threw and caught the ball, and the highest it flew was 12 feet off the ground, then the range is feet.

We can make a function out of this series by using the number of the figure as the input, and the number of squares that make up the figure as its output.

An input of 1 has an output of 1, since figure 1 has just 1 square. An input of 2 has an output of 5, since figure 2 has 5 squares.

An input of 3 has an output of 9, since figure 3 has 9 squares. The inputs to this function are discrete valuesor values that change in increments and not continuously like with the ball-tossing function.