Analyzing Graphs of Functions

1. Analyzing Graphs of Functions Georgia Performance Standard for Algebra Applying Domain and Range graphically and algebraically; using Symmetry to interpret graphs

2. GPS Algebra • MM1A1.c: c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes. • MM1A1.d: d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior • MM1A1.h: h. Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

3. Objective • Students will be able to determine if a graph is symmetricgraphically • Students will be able to determine if a graph is symmetricalgebraically • Students will be able to determine it a function is it is even or odd

4. Essential Questions How do we identify even and odd functions graphically and algebraically?

5. Recall 2.2 • Function • A functionf from a set A to a set B is a relation if each element from set A maps to exactly ONE element of set B. Input: 1, 2, 3, 4, 5 Output: 12, 21, 22, 42, 57, 68, 71

7. Symmetry • Symmetry is when one shape becomes exactly like another if you flip, slide or turn it; "Reflection" (or "Mirror") • OddSymmetry which means the function is symmetric to the origin • Even Symmetry which means the function is symmetric to the y-axis

8. Odd Symmetry • f(x) = -f(x); Sine

9. Even Symmetry • f(x) = f(-x)

10. Examples

11. Things to Remember • Polynomial Symmetry • Even: f(x) = f(-x); y-axis • Odd: f(x) = -f(x); origin (outside function)

12. Any Questions Symmetry

13. Lets look at Algebraically!!

14. Next Class • Vertical Line Test • Translations