1. 1.2 Analyzing Graphs of Functions and Relations

2. Even functions – for every x in the domain of f, f(-x) = f(x)

3. Even functions – for every x in the domain of f, f(-x) = f(x) Odd functions – for every x in the domain of f, f(-x) = -f(x)

4. Ex. 1 Determine whether each function is even, odd, or neither. a
Ex. 1 Determine whether each function is even, odd, or neither. a. f(x) = x3 – 2x

5. Ex. 1 Determine whether each function is even, odd, or neither. a
Ex. 1 Determine whether each function is even, odd, or neither. a. f(x) = x3 – 2x f(-x) = (-x)3 – 2(-x)

6. Ex. 1 Determine whether each function is even, odd, or neither. a
Ex. 1 Determine whether each function is even, odd, or neither. a. f(x) = x3 – 2x f(-x) = (-x)3 – 2(-x) = -x3 + 2x

7. Ex. 1 Determine whether each function is even, odd, or neither. a
Ex. 1 Determine whether each function is even, odd, or neither. a. f(x) = x3 – 2x f(-x) = (-x)3 – 2(-x) = -x3 + 2x = -(x3 – 2x)

8. Ex. 1 Determine whether each function is even, odd, or neither. a
Ex. 1 Determine whether each function is even, odd, or neither. a. f(x) = x3 – 2x f(-x) = (-x)3 – 2(-x) = -x3 + 2x = -(x3 – 2x) So f(x) = -f(x)

9. Ex. 1 Determine whether each function is even, odd, or neither. a
Ex. 1 Determine whether each function is even, odd, or neither. a. f(x) = x3 – 2x f(-x) = (-x)3 – 2(-x) = -x3 + 2x = -(x3 – 2x) So f(x) = -f(x) So ODD

10. b. g(x) = x4 + 2

11. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2

12. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2

13. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x)

14. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN

15. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c
b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c. h(x) = x3 – 0.5x2 – 3x

16. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c
b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c. h(x) = x3 – 0.5x2 – 3x h(-x) = (-x)3 – 0.5(-x)2 – 3(-x)

17. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c
b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c. h(x) = x3 – 0.5x2 – 3x h(-x) = (-x)3 – 0.5(-x)2 – 3(-x) = -x3 – 0.5x2 + 3x

18. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c
b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c. h(x) = x3 – 0.5x2 – 3x h(-x) = (-x)3 – 0.5(-x)2 – 3(-x) = -x3 – 0.5x2 + 3x = -(x x2 – 3x)

19. b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c
b. g(x) = x4 + 2 g(-x) = (-x)4 + 2 = x4 + 2 So g(-x) = g(x) So EVEN c. h(x) = x3 – 0.5x2 – 3x h(-x) = (-x)3 – 0.5(-x)2 – 3(-x) = -x3 – 0.5x2 + 3x = -(x x2 – 3x) So NEITHER