Grades 9/10/11 Introduction to Functions

In this lesson, the graphs of the quadratic function \(f(x)=x^2\), the square root function \(f(x)=\sqrt x\), and the reciprocal function \(f(x)= \dfrac{1}{x}\) will be sketched. The domain and range of each of these functions will also be discussed in relation to the graphs.

In this lesson, we will discuss horizontal and vertical translations and their effect on functions.  We will express translations using function notation and sketch graphs by applying transformations to base functions.

In this lesson, we will discuss reflections in the ‌\(y\)-axis as well as horizontal stretches and compressions, and their effect on functions.  We will express all of these types transformations using function notation and use them to sketch graphs. 

In this lesson, we will discuss reflections in the ‌\(x\)-axis as well as vertical stretches and compressions, and their effect on functions.  We will express all of these types of transformations using function notation and use them to sketch graphs. Comparisons will be made between reflections in the ‌\(x\)-axis and ‌\(y\)-axis, and between vertical and horizontal stretches or compressions. 

In this lesson, we will be discussing all of the types of transformations together. Transformations on a function \(f(x)\) will be identified from the notation \(y=af(b(x-h))+k\) and applied in an appropriate order to sketch graphs.

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.