Exploring Domain and Range of Graphs

The video tutorial covers Objective 1.2, focusing on identifying the domain and range of a relation given a graph. It reviews concepts from Objective 1.1, such as relations and functions, and introduces set builder notation for expressing domain and range. The vertical line test is explained as a method to determine if a graph represents a function. Several examples are provided to illustrate how to find the domain and range of different graphs, emphasizing the importance of understanding open and closed circles in graph interpretation.

Why is a relation defined by a set of ordered pairs considered a function?

• Because the x-values do not repeat

• Because the ordered pairs are unique

• Because the y-values do not repeat

• Because the relation is plotted on a graph

Which of the following ordered pairs, if added to the set, would result in a relation that is no longer a function?

• (1, 2)

• (6, 3)

• (2, 4)

• (5, 1)

What does the vertical line test determine?

• If a graph has a domain

• If a graph has a range

• If a graph is a function

• If a graph is linear

How is the domain of a function represented using set builder notation?

• y such that y is an element of the range

• x such that x is an element of the domain

• x such that x is greater than zero

• y such that y is greater than zero

What is the domain of a graph with arrows on both ends?

• All positive numbers

• All negative numbers

• All real numbers

• All integers

If a graph has no negative y-values and only y-values of 1 and 3, what is the range?

• y such that y > 0

• y such that y = 1 or y = 3

• y such that y < 0

• y such that y is all real numbers

What is the domain of a graph where the smallest x-value is -4 and it goes to infinity?

• x such that x > -4

• x such that x is all real numbers

• x such that x = -4

• x such that x < -4

For a graph with a smallest y-value of 1 and an arrow indicating it goes on forever, what is the range?

• y such that y < 1

• y such that y is all real numbers

• y such that y > 1

• y such that y = 1

What is the domain of a vertical line at x = -5?

• x = -5

• x such that x is all real numbers

• x such that x < -5

• x such that x > -5

If a graph has an open circle at x = 0 and goes on forever to the right, what is the domain?

• x such that x is all real numbers

• x = 0

• x such that x < 0

• x such that x > 0