Exploring Relations, Models, and Functions in Algebra 2

Mrs. Gravakis introduces Algebra 2 Honors students to section 2.1, covering relations, models, and functions. She explains four ways to represent relations: ordered pairs, mapping diagrams, tables, and graphs. The lesson delves into domain and range, emphasizing their importance in understanding relations. Functions are defined as relations where each input has a single output, and the vertical line test is introduced as a method to determine if a graph represents a function. The lesson concludes with an introduction to function notation, highlighting its significance in algebra.

Which of the following is an example of a quadratic relation?

• y = x^2 - 4x + 4

• y = 3x - 5

• y = |x|

• y = 2x + 3

Which of the following is NOT a way to represent relations?

• Ordered pairs

• Mapping diagrams

• Pie charts

• Tables of values

In a mapping diagram, what do the bubbles represent?

• X and Y coordinates

• Inputs and outputs

• Functions and relations

• Graphs and tables

What is the domain of the relation represented by the ordered pairs (1, 2), (3, 4), and (3, 5)?

• {2, 4, 5}

• {1, 3}

• {1, 2, 3}

• {1, 3, 5}

How is the range of a relation typically represented?

• As a set of ordered pairs

• As a list of output values

• As a list of input values

• As a graph

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

• The graph is a quadratic relation

• The graph is a linear relation

• The graph does not represent a function

• The graph represents a function

Which of the following is true for a function?

• Each input has multiple outputs

• Each output has exactly one input

• Each input has exactly one output

• Each output has multiple inputs

What is the function notation for the equation y = 5x + 2?

• x = 5y + 2

• f(y) = 5x + 2

• y = f(x) + 2

• f(x) = 5x + 2

If f(x) = 5x + 2, what is f(3)?

• 20

• 17

• 22

• 15

In the function r(m) = m^2 - 4 + 3m, what is r(-2)?

• 2

• 0

• -6

• 4