You may remember learning about translations in Math 8 and 9. Translations are when graphs can be moved up or down without changing the shape of the graph.

Since all graphs can be derived from either a single or multiple functions, then there must be a way to change the equations of these functions to translate a graph.

Find out what changes to the equation of a function result in horizontal and vertical translations.

**Resources**

- Notes: (see attachments)

**Assignment**

- p15 #1-9, 11, 18

Graphs of functions can be stretched in both the horizontal and vertical directions by the inclusion of a coefficient in front of x or y (also referred to as "replacing x or y").

Note that a stretch can either expand or compress the graph. The term "stretch" simply indicates that the shape of the graph is changing. If the graph is stretched by a factor larger than 1, it is called an "expansion by a factor of *a*". If the graph is stretched by a factor that is smaller than 1, then it is referred to as a compression.

Resources:

- Notes: Stretching the Graphs of Functions

Assignment:

- p15 C1, C2, C3, C4, p28 #1, 3, 4
- p28 #5, 6, 7, 9, 10 13-15, C1 C2 C4 C5

When transforming the graphs of functions, the order in which the transformations occur may matter. Find out when order matters.

Things you should know how to do after today:

- know when the order of transformations matters
- given a combined transformation, determine the individual transformations and the order in which they occurred

Resources

- Notes: Combined Transformations

Assignment:

- p38 #1-8
- p38 #9-11 13 17 C2 C3

What is the horizontal line rule? It's a variation of the vertical line test, of course. Find out what it means to take the inverse of a function and restrict the domain.

Resources

- Notes: Inverse of a Function

Assignment

- p51 #1-6, 8, 9, 12, 15, 20, 21 C1 C2 C3

Things you should know after today:

- how to find the equation for the inverse of a function
- how the coordinates of a function,
*f(x)*, are related to the coordinates of the inverse function,*f*^{-1}(x) - how the graphs of a function and its inverse are like reflections
- how the line
*y=x*is important to reflections, functions and their inverse - the horizontal line rule
- why a domain is restricted when making an inverse
- determine what happens when you do
*f(f*^{-1}(x))