Define, evaluate and compare linear and non-linear functions. (8.F.1-3)
Compare properties of two functions of the same type, each represented in a different way. (8.F.2)
Concepts and Skills
Input-output relationship of functions
* Compare two functions represented differently (table, graph, equation, description)
* Understand, interpret and construct equations in
y=mx+b notation * Describe the relationship between two variables from their graph
Recognize the connection between exponential equations and growth/decay patterns in tables and graphs
Construct equations to express exponential patterns that appear in data tables, graphs, and problem situations
A student in 8th grade will demonstrate the ability to apply and comprehend critical language by understanding, interpreting and constructing linear and non-linear functions.
Linear, exponential and quadratic relationships have specific properties.
Exponential relationships are multiplicative while linear relationships are additive.
Tables, graphs and equations are tools for modeling real-world situations and solving problems.
Factual Guiding Questions
How do you create an input-output table for a given function?
What do each of the variables in the standard equation
y=mx+b represent? What would the graph look like for different types of functions?
What is an exponential equation?
Conceptual Guiding Questions
What is the difference between inputs/outputs of a function versus a relation that is not a function?
How do you compare two functions when looking at tables, graphs, and equations?
How are growth/decay patterns in tables and graphs connected to exponential equations?
Engaging/Debatable Guiding Questions
What is the relationship between linear and non-linear functions?
When would you use the different functions in real-world situations?