# Algebraic Functions

Challenge Project Part 1: Algebraic Functions and Transformations Organize the information in any file type (Word, Power Point, Google Slides, Google doc, etc.) Given the function f(x) = a(x-h) + k, Change the values of a, h, and k one at a time. Step 1: Change the a to 2. What effect does changing the value of a have on the graph when compared to f(x) = x2? Describe in your own words. Step 2: Change the a to 1/2. What effect does changing the value of a have on the graph when compared to f(x) = x2? Describe in your own words. Step 3: Change the h to 4. What effect does changing the value of h have on the graph when compared to f(x) = x2? Describe in your own words. Step 4: Change the h to -4. What effect does changing the value of h have on the graph when compared to f(x) = x2? Describe in your own words. Step 5: Change the k to 5. What effect does changing the value of k have on the graph when compared to f(x) = x2? Describe in your own words. Step 6: Change the k to -5. What effect does changing the value of k have on the graph when compared to f(x) = x2? Describe in your own words. Step 7: Change the a to -2. What effect does changing the value to -a have on the graph when compared to f(x) = x2? Describe in your own words. Step 8: Go to desmos.com. Create a function that incorporates the transformations from steps 1, 3, and 5. Copy and paste/export the graph from desmos.com to your project file to answer #8. Describe the transformations from the parent function y = x2 Step 9: Go to desmos.com. Create a function that incorporates the transformations from steps 1, 4, 6, and 7. Copy and paste/export the graph from desmos.com to your project file to answer #9. Describe the transformations from the parent function y = x2 Step 10: Create a NONQUADRATIC function with at least 3 transformations. Use desmos.com to create a graph of the new function with its parent function on the same grid; and export the graph. State the parent function. Describe the transformations from the parent function. Turn in: Upload file to Canvas Assignment titled: Challenge Project Part 1 Challenge Project Part 2: TRIG GRAPHS AND TRANSFORMATIONS Transformation of Trigonometric Graphs y = Asin[B(x-C)]+D IA is the amplitude The period is 25 Phase (horizontal shift is Period Amplitude Vertical shift is The same applies for the Cosine Function For the Tangent Function, the period is Use the following link to practice with trig graphs and transformations: https://www.nctm.org/Classroom- Resources/Illuminations/Interactives/Trigonometric-Graphing/ Change the values of A, B, C and Done at a time. Using the sin graph provided in the link: Step 1: Change the A to 2. What effect does changing the value of A have on the graph? Describe in your own words. Step 2: Change the A to 1/2. What effect does changing the value of A have on the graph? Describe in your own words. Step 3: Change the B to 2. What effect does changing the value of B have on the graph? Describe in your own words. Step 4: Change the B to 1/2. What effect does changing the value of B have on the graph? Describe in your own words. Step 5: Change the C to 90 degrees. What effect does changing the value of Chave on the graph? Describe in your own words. Step 6: Change the C to 180 degrees. What effect does changing the value of C have on the graph? Describe in your own words. Step 7: Change the D to 2. What effect does changing the value of Dhave on the graph? Describe in your own words. Step 8: Change the D to 1/2. What effect does changing the value of D have on the graph? Describe in your own words. Step 9: Go to desmos.com. Create a new Cosine (cos) trig function that incorporates at least 2 new transformations. Copy and paste/export the graph from desmos.com to this file to answer #9. Describe the transformations from the parent function y = cos x. Step 10: Graph and export the following parent trig functions to this file Sin x Cos x Tan x Sec x Csex Cotx Turn in: Upload file to Canvas Assignment titled: Challenge Project Part 2

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