This lesson unit is intended to help teachers assess how well students are able to translate between graphs and algebraic representations of polynomials. In particular, this unit aims to help you identify and assist students who have difficulties in: recognizing the connection between the zeros of polynomials when suitable factorizations are available, and graphs of the functions defined by polynomials; and recognizing the connection between transformations of the graphs and transformations of the functions obtained by replacing f(x) by f(x + k), f(x) + k, -f(x), f(-x).

The task helps students to focus on vertical and horizontal asymptotes and how they can be used to easily graph simple rational functions. This task prepares students for more complicated rational functions in other tasks.

The shifting of a function to the left or right on a graph is shown in this lesson.

The upwards or downwards of a function on a graph is shown in this lesson.

In this lesson the vertical stretching or squishing of a function on a graph is demonstrated.

In this lesson the horizontal stretching or squishing of a function on a graph is demonstrated.

Students extend what they learned in Module 3 about how multiplying the parent function by a constant or multiplying the x-values of the parent function results in the shrinking or stretching (scaling) of the graph of the parent function and, in some cases, results in the reflection of the function about the x- or y-axis.

Students are expected to do a combination of both, that is, translating and stretching or shrinking of the graph of the quadratic parent function, f(x) = x^2.

Students recognize and use parent functions for linear, absolute value, quadratic, square root, and cube root functions to perform vertical and horizontal translations. They identify how the graph of y = f(x) relates to the graphs of y = f(x)+k and y = f(x + k) for any specific values of k, positive or negative, and find the constant value, k, given the parent functions and the translated graphs. Students write the function representing the translated graphs.

This lesson requires students to explore quadratic functions by examining the family of functions described by y = a (x - h)^2 + k. This lesson plan is based on the activity Tremain Nelson used in the video for Part I of this workshop.

This lesson explains how the graph of a function may be shifted up or down.

The reflection of the graph of a function across the x-axis is discussed in this lesson.

The reflection of the graph of a function across the y-axis is discussed in this lesson.

The purpose of this task is to examine and extend ideas about cubic functions that were surfaced in 3.1 Scott’s Macho March Madness. Students consider a basic cubic function, identifying its characteristics and graph. Students will recognize that the graph can be transformed using the same techniques as quadratic functions. Students will also make other comparisons between cubic and quadratic functions, specifically, their end behavior and the values of each function when # is a fraction.