How do you graph the equation #y= |x-2|-4#?

1 Answer
Jul 2, 2017

Answer:

graph{|x-2|-4 [-10, 10, -5, 5]}

Explanation:

We can easily graph the given function using translation properties of functions.

First, consider what the function #y=|x|# actually means. It represents the absolute value, thus:

# |x| = { (-x, x lt 0), (0, x = 0), (x, x gt 0) :} #

And its graph is therefore:

graph{|x| [-10, 10, -5, 5]}

So then the graph of #y=|x-2|# is the same as the above graph except that it is translated right by #2# units

graph{|x-2| [-10, 10, -5, 5]}

Then finally the graph of #y=|x-2|-4# is the same as the above graph except that it is translated down by #4# units

graph{|x-2|-4 [-10, 10, -5, 5]}