Characteristics of functions

The video tutorial covers key concepts in graph analysis, including domain and range, types of discontinuities, and how to identify increasing, decreasing, and constant intervals. It also explains extrema, boundedness, end behavior, and symmetry in functions, providing a comprehensive understanding of graph characteristics.

What does the domain of a graph represent?

• The set of all possible y-values

• The set of all possible x-values

• The lowest point on the graph

• The highest point on the graph

Which notation is preferred for representing the domain and range of a graph?

• Graphical notation

• Inequality notation

• Interval notation

• Set notation

What type of discontinuity is characterized by a vacant dot on the graph?

• Non-removable discontinuity

• Vertical asymptote

• Horizontal asymptote

• Removable discontinuity

How can you test if a graph is continuous?

• By checking if it has a vertical asymptote

• By drawing it without lifting your pencil

• By finding its domain

• By calculating its range

When describing increasing and decreasing intervals, which symbol should be used?

• Brackets

• Curly braces

• Parentheses

• Angle brackets

What is a relative maximum?

• The highest point on the entire graph

• A point lower than all nearby points

• A point higher than all nearby points

• The lowest point on the entire graph

What does it mean if a graph is unbounded?

• It is symmetrical about the origin

• It is symmetrical about the y-axis

• It has no restrictions on how high or low it can go

• It has a maximum and minimum value

What is the end behavior of a graph?

• The direction the graph heads as it extends left and right

• The highest point on the graph

• The lowest point on the graph

• The symmetry of the graph

How can you determine if a function is even?

• If it has no symmetry

• If it is symmetrical about the origin

• If it is symmetrical about the y-axis

• If it is symmetrical about the x-axis

What does it mean if a function is odd?

• It is symmetrical about the y-axis

• It has no symmetry

• It is symmetrical about the origin

• It is symmetrical about the x-axis