# How do you graph y= absx- 4?

##### 2 Answers
Apr 1, 2015

Start by graphing (or thinking of the graph of) $y = \left\mid x \right\mid$.

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

Now, for $y = \left\mid x \right\mid - 4$ 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) $y = \left\mid x \right\mid$ 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]}

Apr 1, 2015

step1:
Use the definition that $| x | = x$ for $x \ge 0$
and that $| x | = - x$ for $x < 0$

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

$y = x - 4$ , $x \ge 0$
$y = - x - 4$ , $x < 0$

Note that $y = x - 4$ only when $x \ge 0$ 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!