Understanding Domain and Range from Graphs

The video tutorial explains how to determine the domain and range of functions using their graphs. It covers the graph of y = log x, highlighting the vertical asymptote at x = 0 and how it affects the domain, which is x > 0. The range is all real numbers. Another graph with a vertical asymptote at x = 3 is analyzed, showing the domain as x < 3 and the range as all real numbers. The tutorial emphasizes understanding graph behavior to determine domain and range.

What is the domain of a function?

• The set of all possible outputs

• The set of all possible z values

• The set of all possible x values

• The set of all possible y values

What is the vertical asymptote of the graph y = log x?

• x = 0

• x = 1

• y = 0

• y = 1

How is the domain of y = log x expressed in interval notation?

• [0, ∞)

• (-∞, ∞)

• (-∞, 0)

• (0, ∞)

What does the graph of y = log x do as it moves to the right?

• It approaches x = 0

• It approaches y = 0

• It continues indefinitely

• It stops at x = 1

What is the range of y = log x?

• All real numbers

• Positive real numbers

• Non-negative real numbers

• Negative real numbers

How is the range of y = log x expressed in interval notation?

• (-∞, ∞)

• (-∞, 0)

• [0, ∞)

• (0, ∞)

Where is the vertical asymptote for the new graph?

• x = 1

• x = 0

• x = 3

• x = 5

What is the domain of the new graph with a vertical asymptote at x = 3?

• x = 3

• x ≥ 3

• x < 3

• x > 3

What is the range of the new graph?

• All real numbers

• Negative real numbers

• Positive real numbers

• Non-negative real numbers

How does the range of the new graph compare to the first log function?

• It is different

• It is larger

• It is the same

• It is smaller