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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. ο y = x2 and y = π ο What do you notice about the values in the two y-columns? ο Why are all the y-values for y = x2 positive? ο Why do all negative x-values produce an error for y = π ? x 4 2 0 -2 -4 y = x2 x y= π₯ 16 4 0 4 4 2 2 1.41 0 Error Error 16 0 -2 -4 y= 2 x and y = π ο What is the domain of y = x2 and y = π ? ο The domain of y = x2 is all real numbers. ο The domain of y = π₯ is x β₯ 0. ο What is the range of y = x2 and y= π? ο The range of y = x2 is y β₯ 0. ο The range of y = π₯ is y β₯ 0. x 4 2 0 -2 -4 y = x2 x y= π₯ 16 4 0 4 4 2 2 1.41 0 Error Error 16 0 -2 -4 Use the website www.desmos.com/calculator 2 to graph y = x and y = π ο What similarities and differences do you see between these two graphs? ο Both graphs intersect at (0, 0) and (1, 1) ο 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). ο One opens up and one goes to the rightβ¦. ο Why do they intersect at (0, 0) and (1, 1)? y = x2 y= π y= 3 x π and y = π ο Make a prediction about the relationship between y = x3 and y = 3 π₯. ο Both functions will include all real numbers in their domain and range since a cubed number can be positive and negative, as well as the cube root of a number. ο Create data tables for y = x3 and y = π π. (You may use your calculator.) x -8 -2 -1 0 1 2 8 y = x3 -512 -8 -1 0 3 x y= π -8 -2 -1 -2 -1.26 -1 0 1 1.26 2 1 8 0 1 2 512 8 Use the website www.desmos.com/calculator π 3 to graph y = x and y = π ο Use the βfunctionsβ button, select βmiscβ to find the βcube rootβ button. ο What observations can you make about the relationships between y = x3 and y = π π? ο The share the points (0, 0), (1, 1) and (-1, -1). ο The domain and range of both functions are all real numbers. ο They are both symmetric about the origin. y = x3 π y= π