1. Precalculus & Trignometry

2. Objectives:  Recognize the graphs of parent functions.  Right now, you are responsible for  Linear functions  Quadratic functions (squaring function)  The square root function  The cubic function  The cube root function  Reciprocal functions  Absolute Value function  Graph all of the above functions  Differentiate between even and odd functions

3. Even functions  Symmetric with respect to the y-axis

4. Odd functions

5. Linear Functions

6. Graph of the parent linear function

7. Quadratic Functions

8. Graph of the parent quadratic function

9. Square Root Function

10. The parent square root function X values that are not perfect Squares will lead to Irrational y values which are Very difficult to plot

11. Cubic Function

12. Graph of the Cubic Parent Function

13. Cube Root Function

14. Graph of the Cube Root Function Using x values that are not Perfect cubes will result in Irrational y values that are Very difficult to plot.

15. The Reciprocal Function

16. Graph of the Reciprocal Function Do not allow the graph to touch or Cross the x-axis or the y-axis. Plot (1, 1) and draw a curve Plot (-1, -1) and draw a curve.

17. Absolute Value Function

18. Graph of the Absolute Value Function Plot (0, 0) and then graph a Slope of positive 1 to the right And a slope of negative 1 to The left to create a V shape.

19. Practice Graphing

20. Transformations of Parent Functions  Shift functions vertically (up and down)  Shift functions horizontally (left and right)  Stretch and compress functions vertically  Reflect functions over the x and y axis

21. Vertical & Horizontal Shifts just moves the graph does not change shape

22. Example from Desmos

23. Another Example from Desmos

24. Vertical Stretches and Compressions

27. Reflections

28. Desmos Example

29. What you will need to be able to do:  At this point, you should be able to graph al of the parent functions.  You should then be able to look at an equation of a function, know which parent function it represents, and then apply the correct transformations to graph the new function.

30.  You should be able to ignore the “-3” and “+4” and realize that this is just a parabola; however, the parent function has been shifted to the right 3 and up 4 units.  To graph it, you just shift each original point from the parent function right 3 and up 4.

31. Graphs of the example II

33. Graphs

34. A Gift for Making it Through this Presentation  Here’s a chance for bonus. The first 20 emails that I receive with the correct answer will be awarded the bonus points.  You must explain your work in the email to receive credit.  You must also provide me with a written copy of your work when we return to school, or you will lose the bonus points.  Go to the next slide for the problem.

35. A Rose Garden  Suppose that you are working for the mayor of Pittsburgh. Your job is to complete a project that would add a border of yellow roses around an existing rectangular rose garden. The current rose garden is 12 ft long and 5 ft wide and contains only red roses. The yellow rose border should be the same width (thickness) on all 4 sides and should have the same area as the current red rose garden (because the planning committee bought the same number of red and yellow roses to begin with, and we don’t want to waste roses!)  Determine the width of the yellow rose border to the nearest tenth of a foot.

36. A little help ? I want the width/thickness of the yellow rose border. That is the same on all 4 sides. It’s the distance from the outer edge of the red roses to the outer edge of the yellow Rose border. I marked it with a green line for you.