Exploring Domain and Range in Continuous Relations

The video tutorial explains how to find the domain and range of continuous graphs. It covers the use of inequalities and interval notation to represent domain and range, with examples demonstrating different scenarios such as closed and open circles, arrows indicating infinite directions, and bounded values. The tutorial emphasizes understanding the x and y axes as number lines and provides step-by-step solutions for various graph examples.

What does the domain of a continuous graph represent?

• The maximum height of the graph

• The set of all x-values used from left to right

• The length of the graph

• The set of all y-values used in the graph

What symbol is used to represent a value that is not included in the domain or range?

• An open circle

• A cross

• A dot

• A closed circle

If a graph has a closed circle at x = -4, how is this represented in interval notation?

• [-4]

• (-4]

• [-4)

• (-4

In interval notation, what does a parenthesis indicate?

• The value is included in the set

• The value is not included in the set

• The set is infinite

• The set includes all real numbers

How is negative infinity represented in interval notation?

• With a bracket

• With a line

• With a parenthesis

• With a square

What does an arrow in a graph typically indicate?

• The graph stops at this point

• The graph extends infinitely in the direction of the arrow

• The graph changes direction

• The graph has a break in data

What does the domain x < 3 indicate about the graph?

• It only includes x = 3

• It starts at x = 3 and includes all smaller x values

• It extends from x = 3 to positive infinity

• It stops at x = 3 and does not include 3

In a graph where the domain is all real numbers, how is this represented in interval notation?

• 0 to ∞

• R

• [All]

• (-∞, ∞)

What does a domain of x = 4 indicate about the graph?

• The graph is a vertical line at x = 4

• The graph peaks at x = 4

• The graph is a horizontal line at y = 4

• The graph passes through the point (4,0)

How is a range from y = 2 to y = 8, inclusive, represented in interval notation?

• (2, 8]

• [2, 8]

• (2, 8)

• [2, 8)