Recognizing Functions Using the Vertical Line Test

This lesson teaches how to recognize functions using the vertical line test. It covers the definition of functions, representation through ordered pairs, mapping diagrams, and tables. The lesson explains discrete and continuous graphs, their domains, and ranges. It demonstrates the vertical line test to determine if a relation is a function, highlighting special cases and common misunderstandings, such as vertical and horizontal lines.

What is a function in terms of input and output?

• A relation with exactly one output for each input

• A relation with no outputs

• A relation with one input for each output

• A relation with multiple outputs for each input

In a discrete graph, how are the points represented?

• As a single point

• As distinct, unconnected points

• In a continuous curve

• Connected by lines

What does the domain of a continuous graph represent?

• Only a few specific points

• All real numbers

• Only positive numbers

• Only negative numbers

What is the purpose of the vertical line test?

• To find the x-intercept

• To check if a graph is a function

• To calculate the area under a curve

• To determine the slope of a line

If a vertical line intersects a graph at more than one point, what does it indicate?

• The graph is a line

• The graph is a circle

• The graph is not a function

• The graph is a function

Why is a vertical line not considered a function?

• It is diagonal

• It is horizontal

• It has a single y-value for each x-value

• It has multiple y-values for a single x-value

Why is a horizontal line considered a function?

• It is diagonal

• It is vertical

• It has multiple x-values for a single y-value

• It has a single y-value for each x-value