1. Function Breakdown Algebra 2 March 18, 2010

2. Do Now Describe these graphs as sets of transformation on a parent function. What do you notice?

3. Standards A2.1.E * Solve Inverse Variations  I can solve problems that can be represented by inverse variations. A2.5.D Graphs of Cubics  I can sketch polynomials.  I can describe the shape of a polynomial based upon the parent function. A2.5.B Graphs of Square Roots  I can sketch functions with square roots.  I can describe transformation on functions with square roots. A2.5.C Graphs of Inverse Variations  I can sketch functions with inverse variations.  I can describe functions with inverse variations.

4. 3 Possible Actions Graph the function Evaluate a function at x Solve for an x that yields a specific value for f(x).  Often f(x) = 0

5. 3 Actions - Graph See the examples in the next slides.

6. Cubic Functions Graphing a compresses or stretches the graph d is a vertical shift of the graph (in this case, the y-intercept) What do you notice?

7. Inverse Variations - Linear Graphing a compresses or stretches the graph b is a vertical shift of the graph What do you notice?

8. Inverse Variations – Linear 2 Graphing a compresses or stretches the graph b compresses or stretches the graph c is a horizontal shift of the graph What do you notice?

9. Inverse Variations - Quadratic Graphing a compresses or stretches the graph b is a vertical shift of the graph What do you notice?

10. Square Root Functions Graphing a compresses or stretches the graph c is the horizontal shift of the graph d is the vertical shift of the graph What do you notice?

11. Similarities How are all of these similar? All of them have ‘a’ values that stretch or compress. All added (or subtracted) values “outside” of the main function cause a vertical shift. All added (or subtracted) values “inside” of the main function cause a horizontal shift. All of the functions can be used with the same three actions.

12. Stretching and Compressing Why did I always say that a coefficient always stretches or compresses? Shouldn’t it be one or the other? Yes, but if the value is larger than one, it has one effect and if the value is smaller than one, it has the other effect.

13. 3 Possible Actions Graph the function Evaluate a function at x Solve for an x that yields a specific value for f(x).  Often f(x) = 0

14. 3 Actions – Evaluate Evaluate the function when x = 5.

15. 3 Possible Actions Graph the function Evaluate a function at x Solve for an x that yields a specific value for f(x).  Often f(x) = 0

16. 3 Actions - Solve Find the x value that causes the function to equal 3.

17. 3 Actions - Solve Find the zero(s) of the function. No solution. This function has no zeros.

18. Questions?

19. Homework Take Cornell Notes on …  Section 8.4 pp 592 – 596.  Include all “Know It Notes!”  Include all five examples.  Do everyone “Check It Out” problem in your notes (#1 through #5).  Write down any questions that cause you to get stuck.