PARENT FUNCTIONS.pptx
- 1. PARENT FUNCTIONS and TRANSFORMATIONS Presented by: D. Marwa Elsherif
- 2. A function is described as mathematical machine that takes input number “x” and computes output numbers f(x). We then describe the input numbers “x” as being the Domain of the function, while the output numbers f(x) are the Range of the functions. •What is a function?
- 3. •What is a parent function? A parent function is the simplest form of a function. Examples inculde: (line with slope 1 passing through origin) (a V-graph opening up with vertex at origin) (a U-graph opening up with vertex at origin) y x y x y x2
- 5. •Transformations Transformations are shifts up/down, shifts left/right, or a change in size. Ex: Parent Transformations y x y x 2 6 4 2 -2 -4 -6 -5 5 6 4 2 -2 -4 -6 -5 5 y x 2 6 4 2 -2 -4 -6 -5 5
- 6. •Horizontal and Vertical Translations If the parent function is , then … shift up k units shift down k units shift right h units shift left h units y x y x k y x k y x h y x h
- 7. •Example One Graph: ◦ Remember what the parent looks like and go from there… ◦ …the parent shifted right 3 units! y x 3 6 4 2 -2 -4 -6 -5 5
- 8. What would look like? It would shift 2 units left and 1 unit down. •Example Two Graph: The parent shifted down 3 units. y x 3 6 4 2 -2 -4 -6 -5 5 y x 2 1
- 9. •Stretches A stretch multiples all the y-values by the same factor greater than one, stretching the graph vertically (making it skinnier than the parent!) If the parent function is , then a stretch would be provided . y x y a x a 1
- 10. •Shrinks A shrink reduces all the y-values by the same factor less than one, compressing the graph vertically (making it fatter than the parent!) If the parent function is , then a shrink would be when provided . y x y a x 0 a 1
- 11. •Examples Graph the parent function: Graph the transformations: Stretch: y’s are 3 times bigger Shrink: y’s are half as big y 3 x y 1 2 x y x 6 4 2 -2 -4 -6 -5 5 6 4 2 -2 -4 -6 -5 5 stretch parent 6 4 2 -2 -4 -6 -5 5 shrink
- 12. •Reflections A reflection over the x-axis changes the y-values to their opposites…(i.e. the parent flips!) If the parent function is , then a reflection would be . The reflection is over the x-axis ( ) y x y x
- 13. •Example Graph the parent function: Graph the reflection : y x 6 4 2 -2 -4 -6 -5 5 y x 6 4 2 -2 -4 -6 -5 5 reflection parent
- 14. •Describe this transformation y 4 x 2 5
- 15. •Describe this transformation - Solution y 4 x 2 5 6 4 2 -2 -4 -6 -5 5 Shrink (from 4) Shifted right two units (from -2) Shifted down 5 units (from -5)
- 17. WRITE THE EQUATION OF THE PARENT FUNCTION.
- 18. Name That Parent Function!
- 20. Name That Parent Function!
- 22. Name That Parent Function!
- 24. Name That Parent Function!
- 26. Name That Parent Function!
- 28. Name That Parent Function!
- 30. Name That Parent Function!
- 32. Name That Parent Function!
- 35. Name That Parent Function!
- 37. Name That Parent Function!
- 39. Name That Parent Function!
- 41. Name That Parent Function!
- 42. Cube Function
- 43. Name That Parent Function!
- 44. Linear Function
- 45. Name That Parent Function!
- 47. • Presenter: D. Marwa H. Elsherif