GRAPHING CUBIC SQUARE ROOT AND CUBE ROOT FUNCTIONS

GRAPHING CUBIC, SQUARE ROOT AND CUBE ROOT FUNCTIONS

Focus 11 - Learning Goal: Students will be able to construct, compare and analyze function models and interpret and solve contextual problems. 4 In addition to level 3. 0 and above and beyond what was taught in class, the student may: - Make connection with other concepts in math. - Make connection with other content areas. 3 Students will be able to construct, compare, and analyze function models and interpret and solve contextual problems. Function models: - absolute value - square root - cube root - piecewise Analyze multiple representations of functions using: - Key features - Translations - Parameters/limits of domain 2 Students will be able to construct and compare function models and solve contextual problems. Function models: - linear - exponential - quadratic Illustrate the graphical effects of translations on function models using technology. 1 With help from the teacher, the student has partial success with the unit content. 0 Even with help, the student has no success with the unit content.

Use your calculator to create a table of values of the following equations. x 4 2 0 -2 -4 y = x 2 x 16 4 0 4 16 4 2 0 -2 -4 2 1. 41 0 Error

x 4 2 0 -2 -4 y = x 2 x 16 4 0 4 16 4 2 0 -2 -4 2 1. 41 0 Error

What similarities and differences do you see between these two graphs? Both graphs intersect at (0, 0) and (1, 1) The square root function is a reflection of the part of the quadratic function in the first quadrant, about y = x (when x is positive). One opens up and one goes to the right…. Why do they intersect at (0, 0) and (1, 1)? y = x 2

x -8 -2 -1 0 1 2 8 y = x 3 -512 -8 -1 0 1 8 512 x -8 -2 -1 0 1 2 8 -2 -1. 26 -1 0 1 1. 26 2

y = x 3