Identifying Functions in Algebra

Mrs. Spain introduces the concept of functions using a vending machine analogy. She explains functions as input-output machines and introduces the terms domain and range. The video provides examples of functions and non-functions using ordered pairs, tables, mapping diagrams, and graphs. The vertical line test is introduced as a method to identify functions in graphs. The lesson concludes with a review of learning targets and encouragement for students to assess their understanding.

What is the main job of the vending machine in the analogy used to explain functions?

• To accept only coins

• To give a treat based on the button pressed

• To display advertisements

• To dispense different items randomly

What is a function in mathematical terms?

• A relationship where each input is paired with exactly one output

• A machine that dispenses candy

• A set of random numbers

• A graph with multiple lines

What are the terms used to describe the input and output in functions?

• Input and Output

• X and Y

• Start and End

• Domain and Range

In the acronym 'DIX ROY', what does 'D' stand for?

• Domain

• Data

• Diagram

• Distance

Which of the following ordered pairs represents a function?

• {(8, 3), (9, 5), (8, 6)}

• {(4, 6), (5, 1), (4, 6)}

• {(2, 3), (2, 4), (2, 5)}

• {(1, 2), (1, 3), (1, 4)}

Why is the ordered pair set {(8, 3), (9, 5), (8, 6)} not a function?

• Because 8 is paired with two different outputs

• Because 9 is not an input

• Because it has more than three pairs

• Because 3 is not an output

In a mapping diagram, what indicates that it is not a function?

• No arrows at all

• All inputs having the same output

• Arrows crossing each other

• Multiple arrows coming from a single input

What is the purpose of the vertical line test in graphs?

• To measure the distance between points

• To find the slope of the graph

• To determine if a graph represents a function

• To check if the graph is straight

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

• The graph is quadratic

• The graph is linear

• The graph does not represent a function

• The graph represents a function

Which of the following is true for a graph to represent a function?

• Every y-value has exactly one x-value

• The graph must be a straight line

• The graph must be a curve

• Every x-value has exactly one y-value