Unit 1 Description & Learning Goals
In this unit, students will review and extend their understanding of functions from previous mathematics courses. The focus will be on developing a strong foundation for the advanced function types explored later in the course. Students will examine the characteristics of functions, explore different representations, and strengthen their ability to analyze relationships between variables.
Key Learning Goals:
- Review the definition of a function and understand the concept of domain and range.
- Represent functions in multiple forms: algebraic, graphical, and numerical.
- Distinguish between relations and functions.
- Investigate different types of functions, including linear, quadratic, absolute value, and reciprocal functions.
- Explore transformations of functions (translations, reflections, stretches, and compressions.)
- Develop problem-solving skills through real-world applications of functions.
By the end of this unit, you will have the essential tools to describe and analyze a wide variety of functions, laying the groundwork for polynomial, rational, exponential, logarithmic, and trigonometric functions studied later in the course.
Overall Expectations: (from Ontario Curriculum)
D1. demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point;
D2. determine functions that result from the addition, substraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems;
D3. 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.