Students understand set builder notation for the graph of a real-valued function: {(x, f(x)) | x ∈ D}.
Students learn techniques for graphing functions and relate the domain of a function to its graph.

Students understand the meaning of the graph of y = f(x), namely {(x,y) | x ∈ D and y = f(x)}.
Students understand the definitions of when a function is increasing or decreasing.

Students create tables and graphs of functions and interpret key features including intercepts, increasing and decreasing intervals, and positive and negative intervals.

Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for functions addressed in previous modules (i.e., linear, exponential, quadratic, cubic, square root, cube root, absolute value, and other piecewise functions).

Students recognize linear, quadratic, and exponential functions when presented as a data set or sequence, and formulate a model based on the data.

Students create a two-variable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. They interpret the graph and function and answer questions related to the model, choosing an appropriate level of precision in reporting their results.

Students explore quadratic functions by using a motion detector known as a Calculator Based Ranger (CBR) to examine the heights of the different bounces of a ball. Students will represent each bounce with a quadratic function of the form y = a (x - h)^2 + k. This lesson plan is based on the activity Tremain Nelson uses in the video for Part II of this workshop.

Texas Instruments activity where Students graph a quadratic function that models the shape of a bridge trestle and then solve the related quadratic equation by completing the square.

In this lesson, students explore relationships between x-intercepts, factors, and roots of polynomial functions using the graphing calculator. Students also investigate rational functions, identifying the roots and the asymptotes as well as holes in the graphs. Students construct boxes of various dimensions using graph paper, collect height and volume data, and create a scatterplot in order to determine the height of the box with the maximum volume. Students can solve this problem using a graphing calculator or by using their own scatterplots drawn by hand. The use of questioning by the teacher, and the group work of the students are important features of this lesson.

In this Khan Academy activity, students will compare features of linear functions in word problems.

Khan Academy video describing using coordinate plane to divide a line segment into a 3:1 ratio. Interactive drag and drop for estimating point, and button for additional explanation regarding ratio is added.

This lesson is an exploration focusing on the symmetric nature of quadratic functions and their graphs and the interpretation of the key features.

Class activity with scenario where students have to write and evaluate exponential function.

This task is designed for students to practice interpreting key features of functions using graphs, a table of values, and situations. The key features of this task include students:
• Applying their knowledge to interpret key features of functions (domain, range, increasing, decreasing, maximum, minimum, intercepts).
• Practicing writing the domain of a function
• Comparing discrete and continuous situations
• Graphing linear and exponential equations and describing key features of the graph

The purpose of this task is to further define function and to solidify key features of functions given different representations. Features include:

• domain and range
• where the function is increasing or decreasing
• x and y intercepts
• rates of change (informal)
• discrete versus continuous

In this resource, students will determine if a relationship is a function and compare their rate of change and initial value.