Mathematics 2008 JAMB Past Questions - Question 45: If x>0, find the range of the numbers x-3, 3x+2, x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1.

Correct Answer

B

Explanation

Range = H - L= 4x - (x-1)= 4x -x+1To find the range of the numbers x-3, 3x+2, x-1, 4x, 2x-1, x-2, 2x-2, 3x, and 3x+1, we need to determine the minimum and maximum values that these expressions can take.Let's analyze each expression separately:1. x-3: Since x > 0, the minimum value of x-3 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of x-3 is 0-3 = -3. As x can increase without bound, there is no maximum value for x-3.2. 3x+2: Since x > 0, the minimum value of 3x+2 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of 3x+2 is 3(0)+2 = 2. As x can increase without bound, there is no maximum value for 3x+2.3. x-1: Since x > 0, the minimum value of x-1 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of x-1 is 0-1 = -1. As x can increase without bound, there is no maximum value for x-1.4. 4x: Since x > 0, the minimum value of 4x occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of 4x is 4(0) = 0. As x can increase without bound, there is no maximum value for 4x.5. 2x-1: Since x > 0, the minimum value of 2x-1 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of 2x-1 is 2(0)-1 = -1. As x can increase without bound, there is no maximum value for 2x-1.6. x-2: Since x > 0, the minimum value of x-2 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of x-2 is 0-2 = -2. As x can increase without bound, there is no maximum value for x-2.7. 2x-2: Since x > 0, the minimum value of 2x-2 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of 2x-2 is 2(0)-2 = -2. As x can increase without bound, there is no maximum value for 2x-2.8. 3x: Since x > 0, the minimum value of 3x occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of 3x is 3(0) = 0. As x can increase without bound, there is no maximum value for 3x.9. 3x+1: Since x > 0, the minimum value of 3x+1 occurs when x is at its smallest possible value, which is 0. Therefore, the minimum value of 3x+1 is 3(0)+1 = 1. As x can increase without bound, there is no maximum value for 3x+1.In summary, the range of the numbers x-3, 3x+2, x-1, 4x, 2x-1, x-2, 2x-2, 3x, and 3x+1 is:(-3, ∞)= 3x+1