1. The problem asks to determine whether each function is linear or nonlinear based on given data points. 2. A function is linear if the rate of change (slope) between any two points is constant. 3. For Function A, the points are (0,1), (1,2), (2,5), (3,10). 4. Calculate the differences in y and x: Between (0,1) and (1,2): $\frac{2-1}{1-0} = 1$ Between (1,2) and (2,5): $\frac{5-2}{2-1} = 3$ Between (2,5) and (3,10): $\frac{10-5}{3-2} = 5$ 5. Since the slopes are not equal (1, 3, 5), Function A is nonlinear. 6. For Function B, the points are (0,5), (1,4), (2,3), (3,2), (4,1), (5,0). 7. Calculate the differences in y and x: Between (0,5) and (1,4): $\frac{4-5}{1-0} = -1$ Between (1,4) and (2,3): $\frac{3-4}{2-1} = -1$ Between (2,3) and (3,2): $\frac{2-3}{3-2} = -1$ Between (3,2) and (4,1): $\frac{1-2}{4-3} = -1$ Between (4,1) and (5,0): $\frac{0-1}{5-4} = -1$ 8. Since the slopes are constant (-1), Function B is linear. Final answer: - Function A is nonlinear. - Function B is linear.