Exploring Functions and Their Properties

The video tutorial explains how to determine if a relation is a function by checking if each input has a unique output. It covers methods using points, tables, function maps, and graphs. The vertical line test is introduced as a tool for identifying functions in graphs. The tutorial emphasizes the importance of unique outputs for each input to qualify as a function.

What must every input (X) have in a function?

• Its own unique output (Y)

• A repeating output

• Multiple outputs

• No output

In a function, what do we call the X values?

• Outputs

• Inputs

• Equations

• Variables

When checking a list of points, what indicates that it is not a function?

• An X value has different Y values

• All Y values are the same

• All X values are different

• An X value has the same Y value

If an X value repeats in a table, what must be true for it to be a function?

• The Y values must be the same

• The Y values must be different

• The X values must be different

• The table must have an even number of rows

What should you look for in a function map to determine if it is a function?

• Each X value has multiple lines

• Each Y value has one line

• Each X value has one line

• Each Y value has multiple lines

In a function map, what does it mean if an X value has two lines going to different Y values?

• It is a function

• It is not a function

• It is an equation

• It is a variable

What is the vertical line test used for?

• 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

What indicates that a graph is not a function when using the vertical line test?

• The vertical line is horizontal

• The vertical line touches the graph once

• The vertical line does not touch the graph

• The vertical line touches the graph more than once

If a vertical line touches a graph only once at every point, what can we conclude?

• The graph is a curve

• The graph is a line

• The graph is a function

• The graph is not a function

Which of the following graphs would fail the vertical line test?

• A parabola opening upwards

• A straight line

• A circle

• A sine wave