Exploring the Vertical Line Test in Graphs

Professor Von Schmohawk introduces the concept of functions, focusing on real-valued functions of a real variable. The lecture explains independent and dependent variables, domain, and range. It discusses how functions are graphically represented on the Cartesian plane and introduces the vertical line test to determine if a graph represents a function. The lecture also differentiates between binary relations and functions, emphasizing that each domain value must map to a single range value.

What is the output value of a function 'f' called?

• f of x

• f of y

• x of f

• y of f

What is the independent variable in a function?

• The output variable

• The variable that depends on another variable

• The variable that is always constant

• The variable that does not depend on any other variable

What is the set of all valid input values of a function called?

• Range

• Graph

• Output

• Domain

How do we visually represent the infinite set of ordered pairs of a function's graph?

• Using a pie chart

• Using a Cartesian plane

• Using a histogram

• Using a bar chart

What does the graph of a function show?

• How each value maps to multiple values

• How each variable maps to itself

• How each domain value maps to a range value

• How each range value maps to a domain value

What is the vertical line test used for?

• To determine if a graph represents a function

• To determine the range of a function

• To determine the slope of a function

• To determine the domain of a function

What happens if a vertical line intersects a graph more than once?

• The graph represents a quadratic function

• The graph does not represent a function

• The graph represents a linear function

• The graph represents a function

Which type of graph always represents a function unless it is vertical?

• Quadratic graph

• Linear graph

• Cubic graph

• Exponential graph

What are binary relations?

• Relations where each y value can map to multiple x values

• Relations where each y value maps to only one x value

• Relations where each x value maps to only one y value

• Relations where each x value can map to multiple y values

What can be done to a binary relation to make it represent a function?

• Add more values to the domain

• Eliminate parts that cause it to fail the vertical line test

• Rotate the graph by ninety degrees

• Change the range values