Understanding Functions and Rates of Change

The video tutorial explains how to determine if a table represents a function by checking if each input has a unique output. It covers evaluating functions from tables, solving for inputs given outputs, and interpreting real-world data using function tables. Additionally, it demonstrates calculating the average rate of change from tables, using examples related to internet access over time.

What is the main focus when determining if a table represents a function?

• Verifying the table has more X values than Y values

• Confirming the table has no negative values

• Checking if each Y value is unique

• Ensuring each X value has exactly one Y value

Why is it acceptable for Y values to repeat in a function table?

• Because Y values are not important

• Because Y values determine the function

• Because each X value can have multiple Y values

• Because each X value must have exactly one Y value

What makes a table not a function?

• Having more Y values than X values

• Having repeated X values mapping to different Y values

• Having all unique Y values

• Having more X values than Y values

If a table represents a function, what does F(1) signify?

• The X value when Y is 1

• The Y value when X is 1

• The sum of all Y values

• The average of all X values

What does it mean if F(6) is undefined in a function table?

• The table has an error

• The table is not a function

• There is no Y value of 6 in the table

• There is no X value of 6 in the table

How can you find X if given Y in a function table?

• By looking for the Y value in the X column

• By finding all X values that map to the given Y

• By calculating the average of all X values

• By checking if the table is a function

What does it mean if there is no solution for FX = 6?

• There is no X value that maps to Y = 6

• The table is incomplete

• The table has multiple solutions

• The table is not a function

In the context of the word problem, what does M(45) = 40 represent?

• In 1995, 40 million Americans had internet access

• In 1945, 40 million Americans had internet access

• In 1995, 45 million Americans had internet access

• In 1945, 45 million Americans had internet access

How do you interpret M(55) = 172 in the word problem?

• In 1955, 55 million Americans had internet access

• In 2005, 172 million Americans had internet access

• In 1955, 172 million Americans had internet access

• In 2005, 55 million Americans had internet access

What is the average rate of change between 2000 and 2005?

• 13.0 million Americans per year

• 12.3 million Americans per year

• 10.5 million Americans per year

• 11.8 million Americans per year