How do you graph y= absx- 4?

2 Answers
Apr 1, 2015

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]}

Apr 1, 2015

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!