A2-F-1-7

Student Actions

Teacher Actions

• Students will identify the critical points and characteristics of radical functions given a graph, table, set of data or function equations. Students will be able to communicate the mathematically the situational meaning of critical points and key characteristics.

• Students will develop a deep and flexible understanding of the meaning of each critical point and key characteristic  in a radical function, making mathematical and real-world connections.

• Implement tasks that use visual models to support students’ understanding of x- and y-intercepts on a radical function graph.

• Pose purposeful questionsthat go beyond gathering information to probe thinking and require explanation and justification when identifying properties of radical functions..

• Build procedural fluency from conceptual understanding of the properties of function and how they apply to radical functions. Select tasks that provide multiple entry points for tasks on graphing calculators and other appropriate technology.

• Engage students in making connections among mathematical representations by providing students with tasks that involve radical functions in various forms such as graphs, equations, tables, data points, and words.

• Allow time for students to investigate, collaborate, analyze, and generalize the similarities and differences in the graphs of square root and cube root functions and the effects transformations have on square root and cube root parent functions (this may include technology).

Key Understandings

Misconceptions

• Graph square root and cube root functions using various methods and tools, including desmos, a graphing calculator or other technology.

• Identify x- and y-intercepts and key characteristics of square root and cube root functions.

• Recognize the effects of transformations on the parent functions

• Students do not recognize that a cube root function can have a negative radicand and do not graph the negative aspect of the graph.  

• When using a graphing calculator, students may not see the full graph because the window is set too small.

• Students mistakenly try to use a negative radicand in a square root function.

• Students misidentify x- and y-intercepts.