The graph of $y=h(x)$ is a line segment joining the points $(-7,-5)$ and $(-1,-2)$.
Drag the endpoints of the segment below to graph $y=h^{-1}(x)$.
Answer (2)
The problem provides the endpoints of a line segment y = h ( x ) .
To find the inverse function y = h − 1 ( x ) , we swap the x and y coordinates of the endpoints.
The endpoints of h − 1 ( x ) are ( − 5 , − 7 ) and ( − 2 , − 1 ) .
The graph of the inverse function is the line segment joining these points.
Explanation
Understanding the Problem We are given the graph of y = h ( x ) as a line segment joining the points ( − 7 , − 5 ) and ( − 1 , − 2 ) . We need to graph the inverse function y = h − 1 ( x ) . The key idea here is that the inverse function is obtained by swapping the x and y coordinates of the original function.
Finding Endpoints of the Inverse Function The endpoints of the line segment for h ( x ) are ( − 7 , − 5 ) and ( − 1 , − 2 ) . To find the endpoints of the inverse function h − 1 ( x ) , we swap the x and y coordinates.
Calculating the New Endpoints Swapping the coordinates of ( − 7 , − 5 ) gives us ( − 5 , − 7 ) . Swapping the coordinates of ( − 1 , − 2 ) gives us ( − 2 , − 1 ) . Therefore, the endpoints of h − 1 ( x ) are ( − 5 , − 7 ) and ( − 2 , − 1 ) .
Graphing the Inverse Function The graph of the inverse function y = h − 1 ( x ) is a line segment joining the points ( − 5 , − 7 ) and ( − 2 , − 1 ) .
Examples
Imagine you are looking at a map and want to find your way back to your starting point. The inverse function is like retracing your steps. If the original function tells you how to get from point A to point B, the inverse function tells you how to get from point B back to point A. In this case, the line segment represents a path, and the inverse function helps you find the path back by reversing the coordinates.
To graph the inverse function y = h − 1 ( x ) of the line segment connecting points ( − 7 , − 5 ) and ( − 1 , − 2 ) , we swap the coordinates of the endpoints. The new endpoints of the inverse function are ( − 5 , − 7 ) and ( − 2 , − 1 ) . Therefore, the graph of y = h − 1 ( x ) is a line segment connecting these new points.
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