Lesson 3: Solving by Inspection
Duration of Days: 3
Lesson Objective
Students will qualitatively analyze functional relationships by identifying linear and nonlinear features, as well as intervals where a function is increasing, decreasing, or constant, without the need for intensive computation.
How can we determine the nature of a function (linear vs. nonlinear) just by looking at its structure or graph?
How do we describe the behavior of a function over specific intervals?
linear
nonlinear
increasing
decreasing
constant
interval
8.F.A.3: Interpret the equation y=mx+b as defining a linear function.
8.F.B.5: Describe qualitatively the functional relationship between two quantities by analyzing a graph.
This lesson focuses on the qualitative analysis of functions. Students will identify if a function is linear or nonlinear and describe its behavior (increasing/decreasing) based on visual or structural cues (DOK 2).
Misidentifying nonlinear functions as linear.
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