Function Characteristics and Vertical Line Test

The video tutorial explains how to use the vertical line test to determine if a graph represents a function. It includes analyzing four graphs to identify functions and non-functions, and a table exercise to find missing values that demonstrate a non-function. The tutorial concludes with a review of the key concepts and the importance of the vertical line test in understanding functions.

What is the purpose of the vertical line test?

• To determine if a graph is a function

• To find the slope of a line

• To calculate the area under a curve

• To identify the x-intercept of a graph

In Part A, what are you asked to determine about each graph?

• If the graph represents y as a function of x

• If the graph has an x-intercept

• If the graph is a quadratic equation

• If the graph is a linear equation

What does it mean if a vertical line intersects a graph at more than one point?

• The graph is a linear equation

• The graph is a quadratic equation

• The graph is not a function

• The graph is a function

What conclusion can be drawn if a vertical line passes through only one point on a graph?

• The graph is a quadratic equation

• The graph is a linear equation

• The graph is a function

• The graph is not a function

Why is a vertical line not considered a function?

• It has no y-intercept

• It fails the vertical line test

• It passes through multiple points on the x-axis

• It is a horizontal line

What is the result of the vertical line test on the fourth graph?

• The graph is a function

• The graph is a vertical line

• The graph is not a function

• The graph is a horizontal line

What is the overall conclusion from the analysis of the four graphs?

• No graphs are functions

• All graphs are functions

• Only vertical lines are functions

• Only some graphs are functions

In Part B, what is missing from the table?

• A value of y

• A value of x

• A graph

• A function label

What is a key characteristic of a function in terms of input and output?

• Each output has exactly one unique input

• Each output has multiple inputs

• Each input has exactly one unique output

• Each input has multiple outputs

What value of x could make the table not a function if it has outputs of -6 and 8?

• 5

• 7

• 9

• 11