Unit 6
Choosing a function family from data and defending the choice. This unit is where the rest of the course becomes usable.
Lesson 6.1
Choose a model using both the numerical pattern and the context. Equal first differences suggest a linear model, equal second differences at equally spaced inputs suggest a quadratic, and a constant positive output ratio suggests an exponential. A fitted pattern does not justify unlimited extrapolation.
Lesson 6.2
A parameter interpretation must identify its role and units. In a linear model, the intercept is the output at input zero and the slope is change per input unit. In an exponential model, a growth factor applies per chosen time unit. Values outside a plausible context may require a domain restriction.
Lesson 6.3
An intersection solves the equality between two function outputs. A graph helps locate the number and approximate positions of intersections, while algebra can provide exact values. Check each result in the original equation and apply the context domain before accepting it.
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