Question

How do you graph `y= absx- 4`?

Answer 1

Start by graphing (or thinking of the graph of) `y=absx`.

graph{abs (x) [-10, 10, -5, 5]}

Now, for `y=abs(x) - 4` the equations says "find the absolute value of x and then subtract 4 from that number".

So for every `x` value, we find the number (point) `y = absx` and the change `y` by subtracting `4`. This gives us a new point that is a distance of `4` lower than the old point. The end result is, we will move the entire graph down `4`.

graph{abs (x) -4[-10, 10, -5, 5]}

Answer 2

step1:
Use the definition that `|x| = x` for `x >=0`
and that `|x| = -x` for `x<0`

This means, given that,
`y = |x| - 4` this graph is equivalent to the two lines below,

`y = x - 4` , `x>=0`
`y = -x - 4` , `x< 0`

Note that `y = x - 4` only when `x>=0` and

`y = -x - 4` only when `x< 0`

Graph these two lines and you shall get the graph for y = |x| - 4

Don't forget the limitations of each line!