1.2 Analyzing Graphs of Functions and Relations

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1.2 Analyzing Graphs of Functions and Relations

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

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)

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

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)

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

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)

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)

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

b. g(x) = x4 + 2

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

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

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

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

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

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)

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

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 = -(x3 + 0.5x2 – 3x)

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 = -(x3 + 0.5x2 – 3x) So NEITHER