# 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.6  For absolute value, square root, cube root, rational, polynomial, exponential, and logarithmic functions, the student will

a)  recognize the general shape of function families; and

b)  use knowledge of transformations to convert between equations and the corresponding graphs of functions.

Bloom's Level:  Analyze

### 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.61  Recognize graphs of parent functions.

·  AII.6a1  Recognize the general shape of function families.

All.62  Given a transformation of a parent function, identify the graph of the transformed function.

·  AII.6b2  Write the equation of a function given the graph.

All.63  Given the equation and using a transformation approach, graph a function.

·  AII.6b1  Identify the graph of a function from the equation.

·  AII.6b3  Graph a transformation of a parent function, given the equation.

All.64  Given the graph of a function, identify the parent function.

·  AII.6a2  Recognize graphs of parent functions.

All.65  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.6b4  Identify the transformation(s) of a function. Transformations of exponential and logarithmic functions, given a graph, should be limited to a single transformation.

All.66  Using a transformational approach, write the equation of a function given its graph.

·  AII.61  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