You can
put this solution on YOUR website!There are a couple of ways we can graph this.
Solution 1: If you know what the graph of
then you can figure out
:
- The "-" in front of the absolute value causes the graph to be reflected in the x-axis.
- The "+1" causes the graph to be raised up 1 unit.
- Putting these together, the graph of is the graph of reflected in the x-axis and then raised up 1.
Solution 2: Use what you know about absolute value to rewrite
as a piecewise function. (This will make more sense when you see it.) What do we know about absolute value? We know that
- The absolute value of any positive number is itself.
- The absolute value of zero is itself
- The absolute value of any negative number is the negative of its negative self (IOW, the "positive version" of itself)
To put this in algebraic terms:
If
then
If
then
Now we can use these to rewrite
in two ways, one for
and another for
:
If
then
If
then
And we can use these to graph
. On a graph
is on the y-axis and to the right of the y-axis and
is to the left of the y-axis. So we graph
, which is a simple line (slope = -1, y-intercept = 1)
just from the y-axis and to the right. And then, on the same graph, graph
, which is also a simple line (slope = 1, y-intercept of 1),
just to the left of the y-axis.
Either way we should end up with a graph that looks somewhat like an upside down "v" with the point of the "v" at (0,1).
(