Step 3: Sketch the graph:

Question

- Plot the points:
- (0, 0)
- (0.5, 5)
- (1, 5)
- (1.5, 10)
- (2, 10)
- (3, 12)
- (4, 12)
- Continue to (12, 12)

Answer 1

To sketch the graph based on the provided points, we'll first organize the points and then describe how to plot them. Here's a step-by-step approach:

Points to Plot:

1. (0, 0)
2. (0.5, 5)
3. (1, 5)
4. (1.5, 10)
5. (2, 10)
6. (3, 12)
7. (4, 12)
8. (12, 12)

Steps to Sketch the Graph:

1. Set Up Axes:

   • Draw a horizontal axis (x-axis) and a vertical axis (y-axis). Label the axes appropriately.
   • Choose an appropriate scale for both axes. For example, you might label the x-axis from 0 to 12 and the y-axis from 0 to 15 or higher to accommodate your points.

2. Plot the Points:

   • Start plotting each point based on its coordinates:
     • (0, 0): Plot at the origin.
     • (0.5, 5): Move 0.5 units to the right and 5 units up.
     • (1, 5): Move 1 unit to the right and 5 units up.
     • (1.5, 10): Move 1.5 units to the right and 10 units up.
     • (2, 10): Move 2 units to the right and 10 units up.
     • (3, 12): Move 3 units to the right and 12 units up.
     • (4, 12): Move 4 units to the right and 12 units up.
     • (12, 12): Move 12 units to the right and remain at 12 units up.

3. Connect the Points:

   • From (0, 0) to (0.5, 5), draw a line (indicating an increase).
   • From (0.5, 5) to (1, 5), draw a horizontal line (indicating constant value).
   • From (1, 5) to (1.5, 10), draw a line (indicating increase).
   • From (1.5, 10) to (2, 10), draw a horizontal line (indicating constant value).
   • From (2, 10) to (3, 12), draw a line (indicating increase).
   • From (3, 12) to (4, 12), draw a horizontal line (indicating constant value).
   • Finally, draw a horizontal line from (4, 12) to (12, 12) (indicating constant value).

4. Final Touches:

   • Label the important points (if necessary).
   • Make sure to indicate that the graph remains flat at \(y = 12\) from \(x = 4\) to \(x = 12\).

Visual Representation:

Since I can't generate images directly, imagine that your graph will rise sharply from (0, 0) to (0.5, 5), maintain a value of 5 from (0.5, 5) to (1, 5), jump up to 10 from (1, 5) to (1.5, 10), hold at 10 from (1.5, 10) to (2, 10), rise to 12 from (2, 10) to (3, 12), stay at 12 from (3, 12) to (4, 12), and finally, remain flat at \(y = 12\) until \(x = 12\).

This results in a piecewise function shape with segments of rising and flat lines.