Square Roots and Cubic functions

1. Square Roots and Cubic functions

2. Learning Targets • Recognize and describe the following functions: • Square Roots • Cubics • Learn about the locater points for each function and use it to determine transformations, reflections and translations

3. Square Roots • The Parent Function of the square root function is:

4. Square Roots Question to pause and ponder: Why does this graph only go one direction? What does it tell us?

5. Square Roots We cannot have negative inputs within a square root. Try and calculate it on your graphing calculator… Why can’t there be any negatives inputs within a square root? ? ?

6. Square Roots But can’t we have negative outputs? A function has to pass the vertical line test, this means that every function must have exactly one output for every input. Therefore since this is a function our range is limited. ?

7. Square Roots • Characteristics: • Asymmetrical • Restricted domain and range

8. Transformations Lets think about how we can transform, translate or reflect this function? Can we vertically or horizontally translate ? Can we reflect over the x axis? Can we stretch or compress this function?

9. Standard Equation for Vertical Translation Reflects over x-axis when negative Vertical Stretch or Compress Stretch: Compress: Horizontal Translation (opposite direction)

10. Locater Point This is a point on the graph that is used to compare two functions and determine the differences between them. For the Square root function we will use the origin, (0,0), of the parent function.

11. Example #1 How was this function transformed? Vertical Translation: -2 Horizontal Translation:+3

12. Example #2 How was this function transformed? Vertical Translation: +3 Reflected over the x-axis

13. Example #3 How was this function transformed? Vertical Compression

14. Cubics • The Parent Function of the cubic function is:

15. Cubics • Characteristics: • Asymmetrical • No maximum/minimum • Domain and Range is all real numbers

16. Transformations Lets think about how we can transform, translate or reflect this function? Can we vertically or horizontally translate ? Can we reflect over the x axis? Can we stretch or compress this function?

17. Standard Equation for Vertical Translation Reflects over x-axis when negative Vertical Stretch or Compress Stretch: Compress: Horizontal Translation (opposite direction) *Are you starting to see a pattern with these function transformations?

18. Locater Point For the cubic function we will use the origin, (0,0), of the parent function.

19. Example #1 How was this function transformed? Vertical Translation: -4 Horizontal Translation:-4

20. Example #2 How was this function transformed? Horizontal Translation: +1 Reflected over the x-axis

21. Example #3 How was this function transformed? Stretch Factor of 3

22. Determine the Transformations +5 • Helpful Tips: • Determine the function family • Plot the parent graph • Determine the locater point • Compare the transformed graph with the parent graph

23. Homework Worksheet #5