ABSOLUTE VALUES that have to get graphed.

g(x) = | -x - 3 |
f(x) = | x + 2 | + 3
g(x) = | 2x - 3| +1

can you help me do these?
and show the steps?

Of course! I can help you graph these absolute value functions step by step. Here's how you can graph each of them:

1. g(x) = | -x - 3 |
To graph this function, we need to find the critical points, which are the x-values where the expression inside the absolute value changes sign. In this case, -x - 3 changes sign at x = -3.

Step 1: Plot the critical point (-3, 0) on your graph.
Step 2: Choose some additional x-values (e.g., -4, -2, -1, 0, 1) and plug them into the equation g(x) = | -x - 3 | to find the corresponding y-values.
Step 3: Plot each of these points on the graph.
Step 4: Draw a V-shaped line connecting all the plotted points. This line represents the absolute value function.

2. f(x) = | x + 2 | + 3
For this function, the critical point is at x = -2.

Step 1: Plot the critical point (-2, 3) on your graph.
Step 2: Choose additional x-values and find the corresponding y-values.
Step 3: Plot the points on the graph.
Step 4: Draw a V-shaped line connecting all the plotted points.

3. g(x) = | 2x - 3 | + 1
For this function, the critical point is at x = 3/2, which is the solution to 2x - 3 = 0.

Step 1: Plot the critical point (3/2, 1) on your graph.
Step 2: Choose additional x-values and find the corresponding y-values.
Step 3: Plot the points on the graph.
Step 4: Draw a V-shaped line connecting all the plotted points.

By following these steps for each function, you should be able to graph them accurately.