back to *algebra*
# Draw absolute value function y = |x - 4| - 3

- Given:
- Function y = |x - 4| - 3

- Step 1:
- Draw the graph of y = |x - 4|

- Note: when x = 4, y = 0

- Note: The graph of y = |x - 4| is symmetry to the line of x = 4
- Step 2:
- Move the graph of y = |x - 4| down 3 units to get the graph of y = |x - 4| - 3
- Note: when x = 4, y = -3

- Note: The graph of y = |x - 4| - 3 is also symmetry to the line of x = 4

- Therefore,
- for any graph of y = |x - a|
- When x = a, y = 0
- The graph of y = |x - a| is symmetry to the line of x = a
- For the graph of y = |x - a| - b
- When b > 0, move the graph of y = |x - a| down b units to get the graph of y = |x - a| - b
- When b < 0, move the graph of y = |x - a| up b units to get the graph of y = |x - a| - b

- Or you can draw the graph directly