Characteristics of functions

The video tutorial covers key concepts in graph analysis, including domain and range, increasing and decreasing intervals, extrema, boundedness, end behavior, intercepts, and continuity. It explains how to identify and describe these features using appropriate mathematical notation and terminology, preparing students for both free-response and multiple-choice questions.

What is the domain of a graph that extends infinitely in both directions?

• All real numbers

• Only positive numbers

• Only negative numbers

• Numbers between -1 and 1

How is infinity represented in interval notation?

• With curly braces

• With square brackets

• With angle brackets

• With parentheses

When reading a graph from left to right, what does it mean if the graph is going up?

• The graph is constant

• The graph is decreasing

• The graph is undefined

• The graph is increasing

What symbol is used to combine two intervals in interval notation?

• Addition symbol

• Union symbol

• Multiplication symbol

• Intersection symbol

What is a relative maximum on a graph?

• 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

How can you describe a graph that is not restricted in its range?

• Bounded on both sides

• Bounded above

• Bounded below

• Unbounded

What does it mean if a graph is 'bounded above'?

• It extends infinitely downwards

• It extends infinitely upwards

• It has a minimum height

• It has a maximum height

What is the end behavior of a graph that rises to the right?

• It falls to the right

• It rises to the right

• It remains constant

• It falls to the left

Where does the x-intercept occur on a graph?

• Where the graph crosses the y-axis

• Where the graph crosses the x-axis

• Where the graph is undefined

• Where the graph is constant

What type of discontinuity is characterized by a 'hole' in the graph?

• Vertical asymptote

• Non-removable discontinuity

• Removable discontinuity

• Jump discontinuity