Unit 7 Performance Assessment 02

A 20-inch by 15-inch sheet of cardboard is used to create an open-topped box by cutting out squares from each corner and folding the sides up. The side length of the cut out squares is represented by x. Part a) Formulate a function to model the volume of the created box in terms of x, the side length of the cut out squares.

Identify the domain and range of the model function and the domain and range of the problem situation in inequality, set, and interval notation.

How do the domain and range of the model function and the domain and range of the problem situation compare?

What are the x- and y-intercepts of the model function? Are they included in the domain and range of the problem situation? Justify your reasoning.

What is the maximum volume of a box that can be created with this sheet of cardboard? What are the dimensions of this box? What attribute of the graph of the function represents this solution? Justify your reasoning.