Investigating relations and functionsMathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

In earlier grades, students defined, evaluated, and compared functions and used them to model relationships between quantities. In this module, students extend their study of functions to include function notation and the concepts of domain and range. They explore many examples of functions and their graphs, focusing on the contrast between linear and exponential functions. They interpret functions given graphically, numerically, symbolically, and verbally; translate between representations; and understand the limitations of various representations.
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In Algebra I, students have been analyzing the process of solving equations and developing fluency in writing, interpreting, and translating among various forms of linear equations (Module 1) and linear and exponential functions (Module 3). These experiences, combined with modeling with data (Module 2), set the stage for Module 4. Here, students continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions using polynomial function-more specifically quadratic functions as well as square root and cube root functions.
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In Module 5, students synthesize what they have learned during the year by selecting the correct function type in a series of modeling problems without the benefit of a module or lesson title that includes function type to guide them in their choices. Skills and knowledge from the previous modules support the requirements of this module, including writing, rewriting, comparing, and graphing functions and interpretation of the parameters of an equation. Students also draw on their study of statistics in Module 2, using graphs and functions to model a context presented with data and tables of values. In this module, we use the modeling cycle as the organizing structure rather than function type.
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This is an exploratory activity.  Students should have some prior knowledge of evaluating functions for given domain inputs using function notation.This lesson will walk students through using a table and plotting points.  By the end of the lesson students should walk away understanding that a line is infinitely many points.

Students observe patterns between the graph, x-intercepts, factored form, roots, equation, and zeros. They use the patterns they observed and the information given in one column to fill in the other columns.

Representations of FunctionsMathematics Instructional Plans (MIPs) help teachers align instruction with the Mathematics Standards of Learning (SOL) by providing examples of how the knowledge, skills and processes found in the SOL and curriculum framework can be presented to students in the classroom.

In this self-checking activity, students will match 18 cards, identifying the slope, y-intercept, and slope-intercept form of each equation to match each of the six tables.