(15 points) If f(x) = 3x: [a, b] length of [a, b] f([a, b]) length of f([a, b]) ratio [2, 4] 4 − 2 = 2 [2.5, 3.5] 1 [2.9, 3.1] 0.2 [2.99, 3.01] 0.02 [2.999, 3.001] 0.002 Magnification at x = 3 is . (2) (15 points) If f(x) = x 2 : [a, b] length of [a, b] f([a, b]) length of f([a, b]) ratio [2, 4] 4 − 2 = 2 [2.5, 3.5] 1 [2.9, 3.1] 0.2 [2.99, 3.01] 0.02 [2.999, 3.001] 0.002 Magnification at x = 3 is . – 4– MATH 2211 Project 1 (3) (15 points) If f(x) = −x 3 : [a, b] length of [a, b] f([a, b]) length of f([a, b]) ratio [2, 4] 4 − 2 = 2 [2.5, 3.5] 1 [2.9, 3.1] 0.2 [2.99, 3.01] 0.02 [2.999, 3.001] 0.002 Magnification at x = 3 is . (4) (15 points) If f(x) = 1/x: [a, b] length of [a, b] f([a, b]) length of f([a, b]) ratio [2, 4] 4 − 2 = 2 [2.5, 3.5] 1 [2.9, 3.1] 0.2 [2.99, 3.01] 0.02 [2.999, 3.001] 0.002 Magnification at x = 3 is . – 5– MATH 2211 Project 1 (5) (10 points) What do you think the magnification means mathematically? Include any other conjectures you think are true about magnification.