Question

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

Answer 1

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]}