How do you graph #f(x) = | x | - 3#?

Now you can graph

graph{(absx)-3 [-10, 10, -5, 5]}

To graph the function f(x) = |x| - 3:

1. Identify the critical points where the function changes direction. In this case, the critical point is x = 0.

2. Plot the critical point on the graph at (0, -3).

3. Determine the behavior of the function on either side of the critical point:

   • For x < 0, the function becomes f(x) = -x - 3.
   • For x > 0, the function becomes f(x) = x - 3.

4. Plot points on either side of the critical point and connect them to form the graph of the function.

5. Remember that the absolute value function |x| reflects negative values to positive values, so the graph will be symmetric about the y-axis.

6. The resulting graph will resemble two straight lines intersecting at the critical point (0, -3), with slopes of -1 on the left side and +1 on the right side.