Question

How to graph y=|x-4| -3

Answer 1

Okay, let's first establish some ground rules.

1) Whenever something is subtracted or added to x directly, it is a horizontal transformation. In other words, the function is shifted either left or right. Subtraction is right, addition is left.

EX: In y = (x - 4)^2, the function x^2 is moved 4 units to the right.

2) Whenever something is subtracted or added to the whole function, it is a vertical transformation. In other words, the function is shifted either up or down. Subtraction is down, addition is up.

EX: In y = x^2 + 4, the function x^2 is moved 4 units up.

Here, the function |x| is moved 4 units to the right and 3 units down. So, the vertex will be at point (4, -3). Being more technical:

m = -1 if -∞ < x ≤ 4 and m = 1 if 4 < x < ∞

Hope this helps, let me know if I messed up!