This problem is a quadratic function example. The other tasks in this set illustrate F.BF.1a in the context of linear (Kimi and Jordan), exponential (Rumors), and rational (Summer Intern) functions.

The purpose of this task is to give students experience modeling a real-world example of exponential growth, in a context that provides a vivid illustration of the power of exponential growth, for example the cost of inaction for a year.

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

In this task students must figure out how much fresh water you must add to get a particular salt concentration in aquarium water.

The intent of this problem is to have students think about how function addition works on a fundamental level, so formulas have been omitted on purpose.

This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.

This simple conceptual problem does not require algebraic manipulation, but requires students to articulate the reasoning behind each statement.

In this task students are given graphs of quantities related to weather. The purpose of the task is to show that graphs are more than a collection of coordinate points, that they can tell a story about the variables that are involved and together they can paint a very complete picture of a situation, in this case the weather.

These unit conversion problems provide a rich source of examples both for composition of functions (when several successive conversions are required) and inverses (units can always be converted in either of two directions).

Temperature conversions provide a rich source of linear functions which are encountered not only in science but also in our every day lives when we travel abroad. The first part of this task provides an opportunity to construct a linear function given two input-output pairs. The second part investigates the inverse of a linear function while the third part requires reasoning about quantities and/or solving a linear equation.

This task allows the students to compare characteristics of two quadratic functions that are each represented differently, one as the graph of a quadratic function and one written out algebraically. Specifically, we are asking the students to determine which function has the greatest maximum and the greatest non-negative root.

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.

This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

This task presents an opportunity to explore a more general and non-algebraic view of functions.

The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.

This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.

This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.

In this two-lesson unit, from Illuminations, students use a software simulation of one or two runners along a track to investigate and compare constant rates of change. In the first lesson students explore that the time to complete the race is a function of the size of the runner's step. In the second lesson students control the speeds and starting points of two runners, watch the race and examine a graph of the time-versus-distance relationship.