Honors Algebra 2 Function Transformations Discovery

Transcription

1 Honors Algebra Function Transformations Discovery Name: Date: Parent Polynomial Graphs Using an input-output table, make a rough sketch and compare the graphs of the following functions. f x x. f x x. f x x. f x x. f x x. f x x.

2 A parent function is any function where the parameters (real numbers) are identity values of their respective operations. A transformation of a function is an alteration of the function rule that results in an alteration of its graph. For each of the following functions: State the value of a, h, and k. Using your graphing calculator, enter the parent function in and the new function in. Sketch the graph of the parent function and the new function on the same set of axes. Describe the transformations of the parent function to the new function. I. Quadratic Functions: f x a x h k. The parent function is A. Reflection. g( x) x f x. If gx ( ) has a 0, the graph is across the x -axis or vertically. B. Vertical Stretch and Compression. g( x) x. g( x) x. What general conclusion can you make about the effect of the parameter a on the graph of the function? If you want, you may change the value of a on your own to explore further. Vertical Stretch and Vertical Compression If a, the graph is vertically by a factor of a. If 0 a, the graph is vertically by a factor of a.

3 C. Horizontal and Vertical Translations. g( x) ( x ). g( x) ( x ). g( x) x. g( x) x. g( x) ( x ) 0. What general conclusion can you make about the effect of the parameters h function? and k on the graph of the Transformations that move a graph in the coordinate plane are called vertical translations (shift up or down) and horizontal translations (shift left or right).. The transformation of f to g, where f ( x) x and g( x) ( x ) is described as:

4 Continue with the same set of directions on cubic and quartic polynomials. (OK to use Desmos). Sketch the graph of the parent function and the new function on the same set of axes. Describe the transformations of the parent function to the new function. II. Cubic Functions in Vertex Form: f x a x h k. Parent function is f. g x x x g x x. III. Quartic Polynomial: f x a x h k ; Write the parent function: ( ). g x x f x g x x. Given polynomial of the form f x a x h n k, what is the parent function and what are the transformations that occur due to a change in a, h, and k? p x x Parent function: n If a 0, the parent graph has been or. If a, the parent graph has been. If 0 a, the parent graph has been. If h 0, the parent graph has. If h 0, the parent graph has. If k 0, the parent graph has. If k 0, the parent graph has.

5 Honors Algebra Name Applying Transformation of Functions Date Block Put down the technology! ou must complete this assignment without using Desmos or a graphing calculator. Graph a polynomial function using transformations. For each function A. State the parent function B. Describe the transformation that has been applied to the parent graph. C. Graph each polynomial function using transformations (two tables of values).. g x x A. Parent function: a, h, k 0 Table Table h x x A. Parent function: a, h, k 0 Table Table I. For each function

6 A. State the parent function B. Describe the transformation that has been applied to the parent graph.. g x x Parent function: The parent graph has been:. h x x Parent function: The parent graph has been:. j x x Parent function: The parent graph has been:. k x x Parent function: The parent graph has been: II. Write an equation of the function described.. The parent graph of f x x is vertically stretched by a factor of and is translated to the right units and up units.. The parent graph of f x x is reflected across the x-axis, and is translated left units and down unit.. The parent graph of f x x is vertically compressed by a factor of one-half and is translated up units.. The parent graph of f x x is reflected across the x-axis, vertically stretched by a factor of and is translated right units.

7 Honors Algebra Transformation of Functions Practice Name Date Block Put down the technology! ou must complete this assignment without using Desmos or a graphing calculator. Graph a polynomial function using transformations. For each function A. State the parent function B. Describe the transformation that has been applied to the parent graph. C. Graph each polynomial function using transformations (two tables of values).. g x x A. Parent function: a, h, k 0 Table Table h x x A. Parent function: a, h, k 0 Table Table

8 . g x x A. Parent function: a, h, k 0 Table Table h x x A. Parent function: a, h, k Table Table

9 A. Parent function: a, h, k. g x x 0 Table Table A. Parent function: a, h, k. h x x 0 Table Table

10 . g x x A. Parent function: a, h, k 0 Table Table A. Parent function: a, h, k. f x x 0 Table Table