Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions;

• Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically;
• Demonstrate an understanding of the meaning and application of radian measure
• Make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric function and between trigonometric functions and their reciprocals, and use these connections to solve problems
• Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions; evaluate logarithms to simplify numeric expressions.
• Identify and describe some key features of the graphs of logarithmic functions, make connections among the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically;
• Solve exponential and simple logarithmic equations in one variable algebraically, including those in problems arising from real-world applications.
• Determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
• Compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques.

Goal 1: Create a course that illustrates the different functions that were covered in the course.

Goal 2: Describe the course in mathematical detail.

Goal 3: Calculate the average and instantaneous rate of change of the line rider.

Criteria: Each course needs to have the following functions:

• Two different polynomial functions (degree 2 or greater)
• One rational function (that is factorable)
• Sine function
• One logarithmic function
• One composite function (fog)

 

Note: The line rider must ride on at least four of the above functions. The rest can be part of the background (green line).

• Each of the above functions must include the following descriptions in the following order:
• Table of values (15 coordinates determined by Mouse Zoom)
• Equation (curve of best fit determined by Excel or Graphing calculator) and the value of r²
• Zeros (if any)
• Y-intercept
• Vertical Asymptote(s) (if any)
• Other Asymptote (if any)
• Domain and range
• End Behaviors
• Interval of increase
• Interval of Decrease
• Whether or not the function is continuous or discontinuous
• Whether the function is even or odd

Answer rating: 100% (QA)

1 A polynomial function has the form fx a n x n a n1 x n1 a 2 x 2a 1xa 0 The degree of the polynomia... View the full answer