Understanding Domain and Range in Graphs

The video tutorial explains how to model the depth of a toy submarine as a function of time using a graph. It covers the concepts of domain and range, showing how to determine them from the graph. The tutorial also demonstrates how to project the graph onto the horizontal and vertical axes to find the domain and range, and how to express these intervals using interval notation.

What does the graph of the toy submarine represent?

• The distance traveled by the submarine

• The speed of the submarine over time

• The temperature of the water

• The depth of the submarine as a function of time

What is the domain of a function in a graph?

• The set of all possible outputs

• The set of all possible speeds

• The set of all possible inputs

• The set of all possible depths

In the context of the submarine graph, what does the range represent?

• The distance covered by the submarine

• The time it takes for the submarine to reach the surface

• The depth of the submarine at different times

• The speed of the submarine

How can the domain of the function be determined from the graph?

• By analyzing the graph vertically

• By analyzing the graph horizontally

• By measuring the slope of the graph

• By calculating the area under the graph

What is the range of the function in the submarine graph?

• D greater than or equal to -10 and less than or equal to 5

• D greater than or equal to 5 and less than or equal to 10

• D greater than or equal to -5 and less than or equal to 0

• D greater than or equal to 0 and less than or equal to 5

What does projecting the graph onto the horizontal axis help determine?

• The time it takes to reach the surface

• The domain of the function

• The speed of the submarine

• The range of the function

What is the purpose of using interval notation?

• To determine the slope of the graph

• To calculate the area under the graph

• To express the domain and range in a concise form

• To express the speed of the submarine

How is the closed interval from 0 to 7 expressed in interval notation?

• <0, 7>

• (0, 7)

• [0, 7]

• {0, 7}

What do square brackets in interval notation indicate?

• The endpoints are included

• The interval is infinite

• The endpoints are not included

• The interval is open

How is the range from -5 to 0 expressed using interval notation?

• [-5, 0]

• {-5, 0}

• <-5, 0>

• (-5, 0)