Function Transformation Exploration

Size: px

Start display at page:

Download "Function Transformation Exploration"

Allen Terry
5 years ago
Views:

1 Name Date Period Function Transformation Exploration Directions: This exploration is designed to help you see the patterns in function transformations. If you already know these transformations or if you see the trend before you have graphed all the functions, feel free to go directly to the Conclusions at the end of each section. All graphing should be completed with a graphing calculator. Graphing by hand would require too much time! You do not have to sketch the graphs. For each sub-section, graph the parent function in y 1. Keep the parent function in y 1 throughout the sub-section so you can compare the transformed functions. You can graph the transformed functions one at a time in y 2 (my suggestion) or all at once in y 2 y 0. You DO have to complete the Conclusions for each section. You DO have to complete the Application section at the end of the exploration. 1. Identifying Values. In each expressions of the form (x - h), determine the h-value. Example: in (x - 4) the h-value is 4 BUT In (x + 4), the h-value is 4 because (x + 4) can be written as (x - - 4) (x 10) (x 8) (x + 11) (x + 13) (x 21) *************************************************************************************** In each expressions of the form x + k, determine the k-value. Example: in x + 7, the k-value is 7 BUT In x 9, the k-value is -9 because x 9 can be written as x x + 11 x 21 x 78 x f(x - h) A. Quadratic Functions y 1 = x 2 (x + 3) 2 (x + 6) 2 (x + 9) 2 (x - 3) 2 (x - 4) 2 (x - 7) 2 B. Cubic Functions y 1 = x 3 (x + 3) 3 (x + 6) 3 (x + 9) 3 (x - 3) 3 (x - 4) 3 (x 7) 3 C. Square Root Functions Parent Function: y 1 =

2 D. Reciprocal Functions y 1 = E. Exponential Functions y 1 = e x (x + 1) e (x + 5) e (x + 9) e (x - 3) e (x - 6) e (x - 9) e CONCLUSIONS: For any function f(x), if we transform the function into f(x - h), then: When h is positive, the function is translated units to the. When h is negative, the function is translated units to the. 3. f(x) + k A. Quadratic Functions y 1 = x 2 x x x x 2-6 x 2-1 x 2-4 B. Cubic Functions y 1 = x 3 x x x x 3-3 x 3-10 x 3-2 C. Square Root Functions Parent Function: y 1 = D. Reciprocal Functions y 1 = E. Exponential Functions y 1 = e x e x + 3 e x + 5 e x + 7 e x - 4 e x - 6 e x - 5

3 Conclusions: For any function f(x), if we transform the function into f(x) + k, then: When k is positive, the function is translated units (state direction). When k is negative, the function is translated units (state direction). 4. a f(x) {normally written as simply af(x)} A. Quadratic Functions y 1 = x 2 2x 2 4x 2 5x 2-2x 2-4x 2-6x 2 x 2 x 2 x 2 x 2 x 2 - x 2 - x 2 - x 2 B. Cubic Functions y 1 = x 3 2x 3 4x 3 5x 3-2x 3-4x 3-6x 3 x 3 x 3 x 3 x 3 x 3 - x 3 - x 3 - x 3 C. Square Root Functions Parent Function: y 1 = x 2 - x 3 - x 2 - x 3

4 D. Reciprocal Functions y 1 = 4 ( ) = ( ) = - - E. Exponential Functions y 1 = e x 2e x 4e x 5e x - 2e x - 3e x - 6e x e x e x - e x - e x e x e x Conclusions: For any function f(x), if we transform the function into af(x), then: When a is positive, the function (compare shape to parent function) When a is negative, the function (compare shape to parent function)

5 When 1 > a > 0, then the graph is steeper / less steep than the parent function. (circle the correct result) OR: When 1 > a > 0, the graph has a vertical shrink of a factor of. When a > 1, then the graph is steeper / less steep than the parent function. (circle the correct result) 5. f(-x) OR: When a > 1, the graph has a vertical stretch of a factor of. Graph x 2 and (-x) 2 Graph x 3 and (-x) 3 Graph and Graph and Graph e x and e (-x) Conclusions: When we transform f(x) into f(-x), the original function is reflected over the axis. 6. -f(x) Graph x 2 and -(x) 2 Graph x 3 and -(x) 3 Graph and Graph and Graph e x and -e x Conclusions: When we transform f(x) into -f(x), the original function is reflected over the axis. APPLICATIONS: 1. Using your results from above, describe the transformations each function represents from its parent function. Example: Given 5(x 3) The parent function x 2 was translated left 3 units and up 7 units. The function was also made 5 times as steep. (This last statement can be more rigorously stated as: The function has a vertical stretch of a factor of 5.) -2e (x +7) - 4 (-x) 3 8

6 2. Call the graph below f(x). This means we are assuming the graph below is the parent function. Graph the following: a. f(x 3) b. f(x) - 3 c. 2f(x) d. -f(x) e. f(-x)

A. B. C. D. Graphing Quadratics Practice Quiz. Question 1. Select the graph of the quadratic function. f (x ) = 2x 2. 2/26/2018 Print Assignment

A. B. C. D. Graphing Quadratics Practice Quiz. Question 1. Select the graph of the quadratic function. f (x ) = 2x 2. 2/26/2018 Print Assignment Question 1. Select the graph of the quadratic function. f (x ) = 2x 2 C. D. https://my.hrw.com/wwtb2/viewer/printall_vs23.html?umk5tfdnj31tcldd29v4nnzkclztk3w8q6wgvr2629ca0a5fsymn1tfv8j1vs4qotwclvofjr8uon4cldd29v4