This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
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Here are the solutions to your questions: 2) Let the function be defined by f(x) = 2x+1. Complete the table below. The table is already completed correctly based on the function f(x) = 2x+1. For example, when x = -2, f(-2) = 2(-2) + 1 = -4 + 1 = -3. When x = 2, f(2) = 2(2) + 1 = 4 + 1 = 5. |c|c|c|c|c|c| x & -2 & -1 & 0 & 1 & 2 \\ y & -3 & -1 & 1 & 3 & 5 \\ 3) Find the length of a line joining the points a) A=(1,3) and B=(4,7) using the distance formula. Step 1: Recall the distance formula. The distance D between two points (x_1, y_1) and (x_2, y_2) is given by: D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) Step 2: Identify the coordinates of points A and B. A = (1,3) x_1 = 1, y_1 = 3 B = (4,7) x_2 = 4, y_2 = 7 Step 3: Substitute the coordinates into the distance formula. D = sqrt((4 - 1)^2 + (7 - 3)^2) Step 4: Simplify the expression. D = sqrt((3)^2 + (4)^2) D = sqrt(9 + 16) D = sqrt(25) D = 5 The length of the line joining points A and B is 5 units. The final answer is 5. 4) A function is given by y = -2x+3, plot and find the gradient of |AC| and |BE|. Step 1: Complete the table for the function y = -2x+3. • For A (x = -2): y = -2(-2) + 3 = 4 + 3 = 7. So A=(-2, 7). • For B (x = -1): y = -2(-1) + 3 = 2 + 3 = 5. So B=(-1, 5). • For C (x = 0): y = -2(0) + 3 = 0 + 3 = 3. So C=(0, 3). • For D (x = 1): y = -2(1) + 3 = -2 + 3 = 1. So D=(1, 1). • For E (x = 2): y = -2(2) + 3 = -4 + 3 = -1. So E=(2, -1). The completed table is: |c|c|c|c|c|c| Point & A & B & C & D & E \\ x & -2 & -1 & 0 & 1 & 2 \\ y & 7 & 5 & 3 & 1 & -1 \\ Step 2: Plot the function. To plot the function y = -2x+3, you would plot the points calculated above: (-2, 7), (-1, 5), (0, 3), (1, 1), and (2, -1) on a Cartesian plane. Since this is a linear function, connecting these points will form a straight line. Step 3: Find the gradient of |AC|. The gradient m between two points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1). For points A=(-2, 7) and C=(0, 3): m_AC = (3 - 7)/(0 - (-2)) = (-4)/(0 + 2) = (-4)/(2) = -2 The gradient of |AC| is -2. Step 4: Find the gradient of |BE|. For points B=(-1, 5) and E=(2, -1): m_BE = (-1 - 5)/(2 - (-1)) = (-6)/(2 + 1) = (-6)/(3) = -2 The gradient of |BE| is -2. 5) There are how quadrants and Coordinates on the Cartesian Plane. There are 4 quadrants on the Cartesian plane. Coordinates are a set of values (typically an ordered pair (x,y)) that specify the exact location of a point on the Cartesian plane.