Function Fundamentals and Linear Functions | Precalculus, Part 2

Learners will interpret, use, and translate between multiple representations of relations (equation, table, graph, or mapping).
Learners will understand domain and range.
Learners will understand piecewise functions, including absolute value functions.
Learners will know and apply the criteria for which relations are functions (unique output for input, including the visual "vertical line test").
Learners will know and apply the criteria for which functions are one-to-one (unique input for output, including the visual "horizontal line test").
Learners will evaluate functions.
Learners will find average rate of change for a function across a subdomain interval.
Learners will identify subdomain intervals where a function is increasing, decreasing, or constant.
Learners will understand and identify local and absolute extrema and connect local extrema with increasing/decreasing subdomains.
Learners will perform algebraic operations on functions, including composition.
Learners will understand and perform transformation of functions, including shifts, reflections, and stretches, both vertically and horizontally.
Learners will identify functions as even, odd, neither, or both.
Learners will understand and verify inverse functions based on composition of functions.
Learners will understand that functions are fully invertible if and only if they are one-to-one i.e. pass the horizontal line test.
Learners will invert functions algebraically, graphically, and using tables.
Learners will understand linear functions as functions with a constant rate of change.
Learners will understand, find, and interpret slopes, intercepts (x or y), and other points of linear functions.
Learners will find equations for linear functions based on slope and y-intercept, point and slope, two points, or situational information equivalent to any of these.
Learners will find equations for parallel or perpendicular lines.
Learners will translate between graphs and equations for vertical or horizontal lines.
Learners will use exact calculation where applicable, visual estimation with a scatterplot, or technology to fit linear models to problem solving situations. Where technology is used, learners will understand r as a "grade" of the model.
Learners will understand the difference between interpolation and extrapolation and some potential pitfalls of extrapolation.
Learners will use various forms of the slope formula.