Lesson 1: 2-1 Functions and Continuity

How do you know a relation is a function?
What is the difference between a one-to-one function and an onto function?
What is the differences between the graph of a discrete relation and that of a continuous relation?

one-to-one
onto
discrete relation
continuous relation
vertical line test
independent variable
dependent variable
function notation
codomain

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.5 Relate the domain of a function to its graph, an where applicable, to the quantitative relationship it describes.

tbd

Functions can be described as one-to-one or onto. A function is one-to-one if each element of the domain pairs with exactly one unique element of the range. The function is onto if each element of the range corresponds to an element of the domain.

Picture a table that shows the monthly average high and low temperatures in a city. Each month's average temperatures can be represented by the ordered pair (average low, average high). For example March's temperature could be (32, 51)

For excersise 42, suggest that students rewrite the original function by substituting the expression (3d) for each occurrence of the variable x before they begin simplifying.

Instruct a small group of students to write a paragraph describing what is happening in the illustration of the vertical line test in the Key Concept box. Their paragraphs should describe all parts of the diagram in their own words. Ask for volunteers to read their paragraphs. Have students ask for clarification as needed

Use McGraw Hill resources

Use McGraw Hill resources