About this video
In a Khan Academy exercise, h(x) is a line segment from (-8, 1) to (3, -4). To graph h inverse, the video swaps each endpoint's coordinates: h maps -8 to 1, so h inverse maps 1 to -8, and h maps 3 to -4, so h inverse maps -4 to 3. It also shows the inverse is the reflection of h over the line y = x.
You'll be able to
- find points on an inverse graph by swapping the coordinates of points on the original graph.
- graph the inverse of a linear segment using its endpoints.
- explain why the inverse is a reflection over y = x.
Key words
- inverse function
- A function that maps each output of h back to the input that produced it.
- endpoint
- A point at either end of a line segment.
- reflection over y = x
- Flipping a graph across the line y = x, which swaps every point's x and y coordinates.
Transcript
This right over here is our understanding inverses of functions exercise on Khan Academy. It's a good exercise to make sure you understand inverses of functions. It's an interactive one where we can move this line around and it tells us 'the graph of h(x) is the green', so that's this dotted green line, 'the dashed line segment shown below'.
So that's this. 'Drag the endpoints of the segment below to graph h inverse of (x). There's a couple of ways to tackle it. Perhaps the simplest one is we say, okay, look, h(x), what does h(x) map from and to? So h(x), this point shows that h(x), if you input -8 into h of (x), h of -8 is 1, so it's mapping from -8 to 1.
Well, the inverse of that, then, should map from 1 to -8. So let's put that point on the graph, and let's go on the other end. On the other end of h of x, we see that when you input 3 into h of x, when x is equal to 3, h of x is equal to -4. So this point shows us that it's mapping from 3 to -4.
So the inverse of that would map from -4 to 3. If you input -4 it should output 3. Since we took the two end points of this line and found the inverse mapping of it, what I have just done here is that I have graphed the inverse. Another way to think about the inverse is if you were to draw the line y = x, these things should be reflections around the line y =x because one way to think about it is, you're swapping the xs for the ys.
If you were to draw the line y = x, if you flipped it around, the line y = x, the green line, you would actually get the old line. This would flip over there and this would flip over there. But either way, we're done. We have graphed h inverse of x.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.