Unit 1 - Introduction to Functions and Transformations(12 hours)
Unit 1 Description
Students extend their knowledge about characteristics of different functions to key features such as domain, range, maximum/minimum points, number of zeroes of the graphs of functions created by adding, subtracting, multiplying, or dividing functions, and describe factors that affect these properties. Students will also investigate the composition of two functions [i.e., f(g(x))] numerically (i.e., by using a table of values) and graphically, with technology, for functions represented in a variety of ways (e.g., function machines, graphs, equations), and interpret the composition of two functions in real-world applications. Students make connections, through investigation, between the slope of a secant on the graph of a function (e.g., quadratic, exponential, sinusoidal) and the average rate of change of the function over an interval, and between the slope of the tangent to a point on the graph of a function and the instantaneous rate of change of the function at that point.
Learning Goal:
By the end of the unit, you will be able to
- Review and consolidate your knowledge of the properties and characteristics of functions and their inverses.
- Review and consolidate your knowledge of graphing functions using transformations
- Investigate the characteristics of piecewise functions.
- Understand the representations of slope of secant and slope of tangent.
- Understand the composition of functions, their domain and range.
Submission Format: PDF (include your name, date and assignment title); Double spaced, Times New Roman, 12 pt font.