Understanding Functions and Relations

This video tutorial explains the concept of functions, starting with an introduction to ordered pairs and mapping diagrams. It covers how to determine if a relation is a function by ensuring each input has exactly one output. The tutorial includes examples, such as subway ticket pricing, to illustrate these concepts. The video concludes by describing the relationship between zone numbers and ticket prices, highlighting the linear nature of the relationship.

What is one of the success criteria for understanding functions?

• Using functions to create art

• Determining if a relation is a function

• Representing a relation as a set of unordered pairs

• Solving puzzles with functions

In an ordered pair (x, y), what does 'x' typically represent?

• The output value

• The constant value

• The function value

• The input value

How can a relation be represented?

• As a set of ordered pairs or a mapping diagram

• As a graph only

• As a table only

• As a single number

What is the ordered pair for an input of 3 that goes to 9?

• (3, 6)

• (9, 3)

• (3, 9)

• (9, 9)

What defines a function in terms of input and output?

• Each input can have multiple outputs

• Each input has exactly one output

• Each output has multiple inputs

• Inputs and outputs are unrelated

Why is a relation with an input of 0 going to both 5 and 6 not a function?

• Because 5 and 6 are not valid outputs

• Because it has more than one output for a single input

• Because it is a linear relation

• Because 0 is not a valid input

Is the price of a subway ticket a function of the zone number?

• Yes, because all zones have the same price

• No, because prices vary randomly

• Yes, because each zone number has a unique price

• No, because zone numbers are not related to prices

What is the relationship between the zone number and the price of a subway ticket?

• The price doubles with each zone increase

• The price increases by $1.50 with each zone increase

• The price remains constant across all zones

• The price decreases by $1.50 with each zone increase

What type of relationship is described by a constant rate of change in price with zone number?

• Exponential

• Linear

• Cubic

• Quadratic

If the zone number increases by one, how much does the price increase?

• $1.00

• $1.50

• $2.00

• $2.50