Algebra 17 - Vertical Line Test

Professor Von Schmohawk introduces the concept of functions, focusing on real-valued functions of a real variable. The lecture covers the independent and dependent variables, domain, and range. It explains 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 distinguishes between functions and binary relations, emphasizing that functions map each domain value to a single range value. The session concludes with a preview of the next lecture on functions with multiple input variables.

What is the term used for the set of all possible input values of a function?

• Output

• Domain

• Variable

• Range

In a function, what is the variable called whose value depends on the independent variable?

• Dependent variable

• Output variable

• Independent variable

• Constant variable

How is the infinite set of ordered pairs of a function typically represented?

• On a Cartesian plane

• With a pie chart

• Using a number line

• In a table

What is the key condition for a graph to represent a function?

• Each x value maps to exactly one y value

• Each y value maps to exactly one x value

• Each x value maps to multiple y values

• Each y value maps to multiple x values

What test can be used to determine if a graph represents a function?

• Parallel line test

• Vertical line test

• Diagonal line test

• Horizontal line test

What happens if a vertical line intersects a graph at more than one point?

• The graph represents a function

• The graph does not represent a function

• The graph is a linear function

• The graph is a quadratic function

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

• Exponential graph

• Quadratic graph

• Linear graph

• Circular graph