#### Math - 2017-18

# AII.6 and *AII.6 - Transformations

**AII.6** The student will **recognize
**the general shape of function (absolute value, square root, cube root,
rational, polynomial, exponential, and logarithmic) families and will **convert
**between graphic and symbolic forms of functions. A transformational approach to
graphing will be employed. Graphing calculators will be used as a tool to
investigate the shapes and behaviors of these functions.

AII.6For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student willa)

recognizethe general shape of function families; andb)

useknowledge of transformations toconvertbetween equations and the corresponding graphs of functions.

**Bloom's Level:** Analyze

*Adopted: 2009*

### BIG IDEAS

- I can find the correlation between different types of
vehicles and the number of tires they have, the amount of money put into a
vending machine and the kind of selection that comes out, and track the money I
save over a year to determine when I can buy a cell phone.

- I will
recognize that functions are mathematical representations of many input-output
situations.

### UNDERSTANDING THE STANDARD

- The graphs/equations for a family of functions
can be determined using a transformational approach.
- Transformations of graphs include translations,
reflections, and dilations.
- A parent graph is an anchor graph from which
other graphs are derived with transformations.

· The transformation of a function, called a pre-image, changes the size, shape, and/or position of the function to a new function, called the image.

· The graphs/equations for a family of functions can be determined using a transformational approach.

· The graph of a parent function is an anchor graph from which other graphs are derived using transformations.

· Transformations of functions may require the domain to be restricted.

· Transformations of graphs include

Translations (horizontal and/or vertical shifting of a graph);

Reflections (over the *x*-axis and/or *y*-axis); and

Dilations (horizontal or vertical stretching and compressing of graphs).

· The reflection of a function over the line represents the inverse of a function.### ESSENTIALS

__Transformations__

All.6_{1} **Recognize**
graphs of parent functions.

·
AII.6a_{1} **Recognize**
the general shape of function families.

All.6_{2}
Given a transformation of a parent function, **identify** the graph of the transformed function.

·
AII.6b_{2} **Write**
the equation of a function given the graph.

All.6_{3} Given the equation and using a transformation
approach, **graph** a function.

·
AII.6b_{1} **Identify**
the graph of a function from the equation.

·
AII.6b_{3} **Graph**
a transformation of a parent function, given the equation.

All.6_{4} Given the graph of a function, **identify** the parent function.

·
AII.6a_{2} **Recognize**
graphs of parent functions.

All.6_{5} Given the graph of a function, **identify** the transformations that map
the preimage to the image in order to **determine**
the equation of the image.

·
AII.6b_{4} **Identify**
the transformation(s) of a function. Transformations of exponential and
logarithmic functions, given a graph, should be limited to a single
transformation.

All.6_{6} Using a transformational approach, **write** the equation of a function given
its graph.

·
AII.6_{1} **Investigate**
and **verify** transformations of
functions using a graphing utility.

### KEY VOCABULARY

absolute
value, square root, cube root, rational, polynomial, exponential, logarithmic,
transformational, symbolic form, graphic form, parent function, transformed
function, pre-image

*Updated: Oct 27, 2017*