## 12.1.1 Translation of Functions

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
Attachments:
FileDescriptionFile size
12.1.1.notes.functions.pdf12.1.1 Notes.1966 kB
12.1.1.notesHow graphs of functions can be moved left/right or up/down.451 kB

## 12.1.2 Stretches of Functions

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
Attachments:
FileDescriptionFile size
12.1.2.notes.stretches.pdf12.1.2 Notes on Reflections and Stretches1439 kB
12.1.2b.notes.stretches.pdf 1010 kB

## 12.1.3 Combined Transformations

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
Attachments:
FileDescriptionFile size
12.1.3a.notes.pdf 605 kB
12.1.3b.notes.pdf 2174 kB

## 12.1.4 Inverse of a Function

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))
Attachments:
FileDescriptionFile size
12.1.4.notes.inverse.pdf 441 kB

## 12.1.5 Review

Assignment

• p56 #1-17
• Make your cheat sheet for your test (one side, one half page)

Attachments:
FileDescriptionFile size
12.1.5.warmup.a.pdf 94 kB
12.1.5.warmup.b.pdf 222 kB