Determining Functions from Tables and Graphs

The video tutorial explains the concept of functions, how to identify them from tables and graphs, and introduces the notation used in mathematics. It uses examples like a function machine to demonstrate how to derive equations from input-output pairs. The tutorial also covers more complex function puzzles and how to analyze input-output tables. Finally, it shows how to determine functions from graph lines, providing a comprehensive understanding of functions in mathematics.

What is a function in mathematical terms?

• A rule that only applies to independent variables

• A specific relationship between independent and dependent variables

• A rule that only applies to dependent variables

• A random relationship between variables

What does 'f(x)' represent in mathematics?

• A different concept from 'y'

• The function of y

• A constant value

• The same as 'y'

If you input 2 into a function machine and get 6, which of the following could be the function?

• y = x + 4

• y = x + 2

• y = 3x

• y = 2x

If you input 7 into a function machine and get 11, which function is likely correct?

• y = 2x + 1

• y = x + 3

• y = 3x

• y = x + 4

What is the function if inputting 2 gives 5, 5 gives 11, 6 gives 13, and 9 gives 19?

• y = 3x

• y = x + 4

• y = 2x + 1

• y = x + 3

What is the rule for the function if inputting 1 gives 5, 2 gives 10, and 3 gives 15?

• y = x + 6

• y = x + 5

• y = 5x

• y = x + 4

What is the function if inputting 2 gives 0, 3 gives 1, and 4 gives 2?

• y = x + 1

• y = 2x

• y = x + 2

• y = x - 2

What is the function if inputting 1 gives 5, 2 gives 6, and 3 gives 7?

• y = x + 4

• y = x + 5

• y = x + 6

• y = x + 1

How do you determine the function of a line on a graph?

• By looking at the color of the line

• By finding points and analyzing their relationships

• By measuring the length of the line

• By guessing the values

What is the function of a line if the points are (0, 1), (2, 3), (4, 5), and (6, 7)?

• y = x + 3

• y = x + 4

• y = x + 2

• y = x + 1