Students will use algebraic functions on a coordinate grid to create a work of math art. Students will be expected to use at 10 different “curves” including at least 3 different types of functions. Students will identify the different curves by equation, give the domain and range for that curve, and describe how the curve used has been transformed from the parent function for that type of curve. This problem is designed to give students mastery over limiting domain and range of functions as well as understand how transforming functions alters the size, shape, position, and direction of their graphs. Students will be expected to provide color to their artwork, but this is much more than just creating a pretty picture.
Students will learn about the different types of math functions.
Students will learn how to write a limited domain and range for a piece of a function.
Students will learn how to describe transformations of functions and how they appear in graphs and equations.
Students will learn how to graph functions with precision through exact points rather than simply sketch an approximate shape/curve.
1. Quiz on identifying parent functions by equation and graph.
2. Exit ticket – what in the equation influences the shape of the curve that a function makes?
1. Practice problems
2. Quiz on the domain and range of parent functions and domain and range of pieces of functions.
1. Journal – describe the effects of changing f(x) = x to g(x) = x + b, f(x) = x to g(x) = a(x), etc.
2. Class discussion – which types of functions are the hardest to incorporate into a picture?
1. progress log – which functions are being used in the project and what will the final product look like.
2. Class discussion – why aren’t circles or sideways parabolas functions? How can I use pieces of multiple functions to create the same effect?
3. Exit ticket – rough draft – sketch of artwork on graph paper provided.
Direct instruction presenting the different functions. Brainstorm – what is causing these changes in the appearance of the curve?
Modeling – begin with domain and range of parent functions that often include all real numbers. What if I don’t want the whole function? How can I limit it or “cut off” the domain?
Use technology to demonstration of the effects of changing the parameters of a function on its graph.
Model finding and graphing exact points – either by using the transformations from the parent function or by substituting values for x and creating a table.
students can brainstorm for ideas; log their progress; evaluate their product; describe their difficulties.
the class may discuss which functions are the most difficult to use and why.
