Content Standards and Benchmarks:
I,1,4: Explore patterns (graphic,
numeric, etc.) characteristic of families of functions; explore structural patterns within systems of objects, operations
or relations.
III, 2, 2: Locate
and describe objects in terms of their orientation and relative position, including displacement (vectors), phase shift, maxima,
minima, and inflection points; give precise mathematical descriptions of symmetries.
Objective:
After reading the lesson the night before, and hearing my lecture regarding graphs of transformations of functions, students will be able to transform and graph functions using translations of x and y and scale-changes
of x and y.
Anticipatory
Set:
Show students pictures of different size changes on the OH. Also have
student stand up and move around to simulate translations in different directions. The
other students will determine where they move.
Input:
Ø Graph Translation Theorem (Pg 196): Th,k: (x,y) à (x+h, y+k), So replace x with x-h and y with y-k
Ø Equation of a circle: x2 + y2 = r2
Ø Graph Scale-Change Theorem (Pg 196): Sa,b: (x,y) à (x/a, y/b), So replace x with x/a and y with y/b
Ø Graph-Standardization Theorem (Pg198)
If T: (x,y) à (ax + h, by + k),
then in parametric form x=f(t) and y=g(t)
is transformed to x=af(t) +h and y=bg(t) +k
Ø Know parent functions so you can determine what the transformations are.
Modeling:
v As I lecture on what the lesson covered, I will do examples of the different transformations
on the board.
Guided Practice:
Students will guide me through the questions they have on the lesson
Independent practice:
v Students will be given Lesson Master 3-8 for extra practice and they
will be assigned lesson 3-9 to read and do the C.A.R. problems for the next day.
Closure:
Ø Review with students what they need to know about
transformations of functions:
- What parent functions are.
- How to translate and scale-change
- New notation of transformations
