advanced mathematic assignment
Curriculum Connection, Learning Goals and Success Criteria
Curriculum Connection:
· identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;
· solve problems involving polynomial equations graphically and algebraically;
· demonstrate an understanding of solving polynomial inequalities.
Chapter Overview and Learning Goals:
Linear and quadratic functions are members of a larger group of functions known as polynomial functions. In business, the revenue, profit, and demand can be modelled by polynomial functions. This chapter focuses on the properties and key features of graphs of polynomial functions and their transformations. You will also learn about the concepts of average and instantaneous rate of change.
1 Power Functions
2 Characteristics of Polynomial Functions
3 Equations and Graphs of Polynomial Functions
4 Transformations
5 Slopes of Secants and Average Rate of Change
6 Slopes of Tangents and Instantaneous Rate of Change
Success Criteria:
1 I am able to recognize polynomial expression and the equation of a polynomial function, and identify linear and quadratic functions as examples of polynomial functions;
2 I am able to compare the numeric, graphical, and algebraic representations of polynomial functions;
3 I am able to describe key features of the graphs of polynomial functions;
4 I am able to distinguish polynomial functions from sinusoidal and exponential functions;
5 I am able to determine the equation of polynomial function that satisfies a given set of conditions;
6 I am able to explain the properties of an even and odd polynomial functions and determine whether a given polynomial is even, odd, or neither;
7 I am able to calculate and interpret the average rates of change of functions, given various representations of the functions;
8 I am able to make connections between average rate of change and slope of a secant, and instantaneous rate of change and the slope of a tangent;
9 I am able to recognize examples of instantaneous rates of change arising from real-world situations;
I am able to solve real-world problems involving average and instantaneous rate of change.