Math - 2018-19
AII.6 - Abs Value Transformations
AII.6 For absolute value,
square root, cube root, rational, polynomial, exponential, and logarithmicfunctions, 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.
- 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
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.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
the general shape of function families.
the equation of a function given the graph.
the graph of a function from the equation.
· AII.6b3 Graph a transformation of a parent function, given the equation.
graphs of parent functions.
the transformation(s) of a function. Transformations of exponential and
logarithmic functions, given a graph, should be limited to a single
and verify transformations of
functions using a graphing utility.
value, square root, cube root, rational, polynomial, exponential, logarithmic,
transformational, symbolic form, graphic form, parent function, transformed