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(male narrator) In this video,
we're going to look at how we can graph
the inverse of a function.
If we know that inverse functions simply switch...
the x and y values, or input and output values,
what we can do is identify key points on the graph...
and then switch the coordinates...
to get the coordinates of the inverse function.
Let's take a look at some examples
where we identify those key points
and switch them to get our inverse graph.
In this problem, we see a graph with two end points
and also a key point where the graph seems to bend.
Let's take a look at the coordinates of those points.
The point on the far left is found
by going left three, up four.
This makes that first point: -3,4.
To graph the inverse of this point,
we'll switch those coordinates to get 4,3...I'm sorry, 4,-3.
And we can graph 4,-3;
and this is the point on our inverse graph.
Let's take a look at the next point--
this bending point in the middle.
The coordinates of that point are one to the right and two up.
To graph the inverse,
we'll switch those points to get 2,1.
And we'll graph 2,1 on our inverse graph.
The other key point is the last end point,
and we see that is
at three to the right and four down, or -4.
Taking 3,-4 and switching those values,
we get our second point at -4,3.
Graphing -4,3, we end up with our new points,
and we can connect those points using the same pattern.
And we get our inverse graph.
Let's take a look at another example
where we find the inverse graph by identifying key points
and switching the order of the coordinates.
Again, we might start by doing the point on the far left.
You'll notice that's at the point left four, down two;
or -4,2...
-2, sorry...because we went down 2.
To switch those orders, we would have -2,-4;
or two to the left and four down.
Our next key point might be the point at the peak.
This point is to the left one: -1;
and up four: -1,4.
When we switch the order of those points,
we get 4,-1.
This means we'll go four to the right and one down
to get our next key point.
Finally, the graph ends down here to the right
at the point 4,-2.
When we switch the order of those coordinates,
we end up with -2,4; and we'll graph -2,4...
to complete our inverse graph.
By connecting the dots, this graph is the graph
of the inverse of the original graph.
As you can see, we can quickly graph the inverse of a function
by identifying a few key points
and switching the order of the coordinates,
because the inverse simply switches x and y.