F(x) = 3x+2, x≤2 f(x) = -0,5x-3, -2

To sketch the graph of the function f(x), we can start by determining the key points and then connecting them.

1. For x ≤ 2: f(x) = 3x + 2

   • Take a few values of x, such as x = 0, 1, and 2.
   • For x = 0, f(0) = 3(0) + 2 = 2.
   • For x = 1, f(1) = 3(1) + 2 = 5.
   • For x = 2, f(2) = 3(2) + 2 = 8.
   • These points give us the line segment from (0, 2) to (2, 8).

2. For -2 < x < 0: f(x) = -0.5x - 3

   • Again, take a few values of x, such as x = -1, -0.5, and -0.1.
   • For x = -1, f(-1) = -0.5(-1) - 3 = -2.5 - 3 = -5.5.
   • For x = -0.5, f(-0.5) = -0.5(-0.5) - 3 = 0.25 - 3 = -2.75.
   • For x = -0.1, f(-0.1) = -0.5(-0.1) - 3 = 0.05 - 3 = -2.95.
   • These points give us a downward sloping line segment.

3. For x ≥ 0: f(x) = -5

   • The value of f(x) is constant and equal to -5 for all values of x greater than or equal to 0.
   • This gives us a horizontal line at y = -5.

Now, we can combine these segments to sketch the graph of f(x).

• Draw a line segment from (0, 2) to (2, 8).
• Draw a downward sloping line segment from (-1, -5.5) to (-0.5, -2.75) to (-0.1, -2.95).
• Draw a horizontal line segment from (0, -5) to the right.

This completes the sketch of the graph of f(x).