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4 different equations of functions each representing from a different function family. All functions represented in the same graph. Students play with calculators inputting values to see which correspond to the appropriate function in the graph.

This Illustrative Mathematics task assesses if students can construct a trigonometric model that represents a context.

Students sketch the parent function and then sketch different transformations of that function to compare them.

This task focuses on using Carbon 14 isotope exponential decay to date when plant died. If plant died at a certain time, how much Carbon 14 should still be present?

A table comparing the populations of three different cities every 10 years. Students figure out which family of functions best models each city.

Students use equations, graphs, and tables to compare linear, exponential, and quadratic functions. As students compare the functions they should use rate of change and end behavior to help differentiate the function families and their unique properties. Meant to be supported with some kind of graphing technology whether graphing calculators, Desmos, Geogebra, or some other similar tools.

Students compare three functions: f(x)=2x, g(x)=x² and h(x)=2^x and analyze rates of change. It would be good to modify the activity by having students also graph and create tables for the three functions then describe how they compare in each of those representations.

These four questions can help you surface how students understand finding rate of change from a set of graphs.

This Illustrative Mathematics task asks students to construct a pair of related trigonometric models to solve a contextual problem.

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Students are given a situation about a flag being raised and several graphs. They have to explain why each graph might work and what is going on to model the situation.

Students are given Moore's prediction for how quickly memory storage would grow for computers and then given data for different years on average PC storage capacity. Students need to see how their function based on Moore's predictions compares to real life data and continually refine based on subsequent years. Teachers might want to encourage students to also create graphs and tables with this activity.