Functions – First Draft

I won’t start teaching functions for a few weeks at least, but I want to get it right, and I’m thinking about what that part of the year is going to look like. This is a first draft.

Linear functions:
Start with linear equations — moving from proportional relationships to general linear relationships, graphing, modeling with linear equations, slope/y-intercept, and rates of change.

Functions intro:
Introduce function notation, what distinguishes a function, and domain and range. Apply these properties to simple piece-wise functions and graphing stories, including linear function and rate of change concepts.

Sequences:
Linear sequences, recursive sequences, and visual patterns. Visual patterns will introduce quadratics. Also review domain and range as they apply to sequences.

Quadratics:
Graphing quadratics, properties of quadratic graphs, forms of quadratics and how those are related to maximum, minimum, and zeros. Modeling with quadratics. Manipulating polynomials.

Exponentials:
Difference between linear and exponential growth. Graphing exponential growth, properties of exponential functions, parts of exponential functions.

Meta-Functions:
Choosing the appropriate type of function for modeling purposes, comparing functions, of similar and different types, systems of functions, advanced function properties — even/odd, inverses, more piece-wise functions, modeling with functions, analysis of function types.

Function Transformations:
Horizontal and vertical shifts, multiplicative transformations, analyzing properties of transformations, modeling using function transformations.

That’s what I have. There will likely be some other units not focused on these topics tossed in, but maybe not, and this will also likely be revised along the way. But I’m excited about this unit -I have a pretty good store of tasks, from Desmos lessons, to 3-acts, and more, and I think it will be a fun unit.

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