Defining the graph of a function, vertical line test, characteristics of graphs, approximating relative extrema, and even and odd functions are covered with examples that include charts and graphs.

In this task, students are asked to analyze a function and its inverse when the function is given as a table of values. In addition to finding values of the inverse function from the table, they also have to explain why the given...

In this task, students interact with a Desmos app by moving sliders and making observations about features of the graphs and the structures of the expressions of the functions. Aligns with F-IF.C.7.d.

This task addresses an important issue about inverse functions. In this case, the function f is the inverse of the function g but g is not the inverse of f unless the domain of f is restricted. Aligns with F-BF.A.1.c.

The purpose of this task is to examine trigonometric functions for obtuse angles. Aligns with F-TF.A.2.

In this task about parking lot rates, students investigate what a function is and explain their reasoning. Aligns with F-IF.A.1.

In a video game called Snake, a player moves a snake through a square region in the plane, trying to eat the white pellets that appear. This task has learners approach a function via both a recursive and an algebraic definition, in the...

In this task involving temperature conversions, students construct a linear function given two input-output pairs, investigate the inverse of a linear function, and reason about quantities and/or solving a linear equation. Aligns with...

Students are presented with a table that shows the populations of foxes and rabbits in a national park over a 12-month period. This is the second Foxes and Rabbits task. In this problem, students must find trigonometric functions that...

In this task, students use trigonometric functions to model the movement of a point around a wheel and through space. Students also interpret features of graphs in terms of the given real-world context. Aligns with F-TF.B.5 and F-IF.B.4.

The context of this task is that a quarter was put into a bank account in 1901 and students are asked to calculate its value in 2013 at two different interest rates. Those amounts are compared to the appreciation rate of a rare and...

In this task, learners are shown a table of U.S. population data between 1790 and 1860 and are asked to explore whether exponential functions would be appropriate to model relationships within the data. The purpose of the task is to help...

In this task, students prove that linear functions grow by equal differences over equal intervals, and notice that in this case, the equal differences have the same value as the slope. Aligns with F-LE.A.1.a.

This problem examines the growth of algal blooms in Chesapeake Bay. Students build an exponential function modeling algae concentration based on the information provided, and gain an appreciation for the exponential growth exhibited...

In this task, students investigate the relationship between linear equations and linear functions. Aligns with F-LE.A.2.

Students are shown two tables of data showing the approximate boiling point of water at different elevations. Both data sets can be modeled by linear functions but with different slopes. When the tables are combined, however, students...

In this task, students work with exponential functions in a real-world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve...

In this task about the height of baseballs thrown into the air, students are asked to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out...

This is the first of a series of problems building to an understanding of an important property of polynomial functions, that a polynomial of degree d can have at most d roots. Aligns with A-APR.B.2.

In this problem about the predator-prey relationship between the fox and rabbit populations, 8th graders are asked to identify and explain any functions that they see. Aligns with 8.F.A.1.

In this task, students are presented with four functions and must determine whether each is odd, even, or neither. Includes a GeoGebra worksheet that can be used by the instructor to demonstrate the material. Aligns with F-BF.B.3.

In this task, 8th graders are presented with the equation for a linear function and asked to identify which of six problem situations the equation could represent. Aligns with 8.F.B.

The purpose of this task is to apply translations and reflections to the graphs of the functions f(x)=cos x and g(x)=sin x in order to derive some trigonometric identities. There are also rotations 180 degrees about points on the x-axis...

The goal of this task is to examine some population data for large cities from a modeling perspective. Students are asked to decide if the population data can be accurately modeled by a linear, quadratic, and/or exponential function, and...