#### Math - 2018-19

# AII.6 - Quadratic Transformations

AII.6For (quadratic)~~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.

*Adopted: 2016*

### 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 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

**The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to**

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

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

·
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.

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

·
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.

·
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: Aug 23, 2018*