Name ____________________________ Date ______________ Period _______ U2 – S1 – L5 Transformations of Functions: Use Desmos # 1- 7 Identify the type of function, the Parent Function, and describe the transformation represented. 1. g(x) = x 2 – 1 Type: ________________________________Parent Function: __________________ Transformation:________________________________ 2. f(x) = 2 x 1 Type: ________________________________Parent Function: __________________ Transformation:________________________________ x2 Type: ________________________________Parent Function: __________________ Transformation:________________________________ 3. h(x) = 4. g(x) = x3+ 3 Type: ________________________________Parent Function: __________________ Transformation:________________________________ 5. g(x) = x  6 Type: ________________________________Parent Function: __________________ Transformation:________________________________ 6. f(x) = x  5 - 2 Type: ________________________________Parent Function: __________________ Transformation:________________________________ 7. h(x) = 1 2 x 5 2 Type: ________________________________Parent Function: __________________ Transformation:________________________________ #8-12 Identify the domain and range of the function in set & interval notation. Describe the transformation from its parent function. 8. g(x) = 3 x Domain : _____________________ Range : ___________________ Transformation:_____________________________________________ 9. h(x) = - x2 + 1 Domain : _____________________ Range : ___________________ Transformation:_____________________________________________ 10. h(x) =  x  2 Domain : _____________________ Range : ___________________ Transformation:_____________________________________________ 11. f(x) = 3 3 x 4 Domain : _____________________ Range : ___________________ Transformation:_____________________________________________ 12. h(x) = x+9 Domain : _____________________ Range : ___________________ Transformation:_____________________________________________ #13 - 17 Given the parent function and a description of the transformation, write the equation of the transformed function, f(x). 13. Absolute value—vertical shift up 5, horizontal shift right 3. ____________________ 14. Square Roots —Two units left, seven units up ____________________ 15. Cubic—decreases and vertical shift down 2 ____________________ 16. Absolute value – expanded “v” shape, 3 right, 1 down ____________________ 17. Quadratic—contracted, horizontal shift left 8. ____________________ 18. Which graph best represents the function f(x) = 2x2 - 2? a. b. c. ________________ d. 19. Name the six parent functions that we are studying. ______________________ _____________________ ___________________ ______________________ _____________________ ___________________ 20. Create a transformation and describe how it is translated from the parent function. a) Linear – ____________________________________ Transformation: ______________________________________ b) Absolute Value - ____________________________________ Transformation: ______________________________________ c) Quadratic - ______________________________________ Transformation: ______________________________________ d) Cubic - _____________________________________ Transformation: ______________________________________ e) Square Root - _____________________________________________ Transformation: ______________________________________