The inverse of graph A is not a function, but the inverses of graphs B and C are functions.
Graph A
The inverse of graph A is not a function because for a single input value, there are two output values.
For example, at the input value 0, the output values are 1 and -1.
This means that the graph of the inverse function would pass through the same point twice, which is not allowed for a function.
Graph B
The inverse of graph B is a function because for every input value, there is exactly one output value.
This can be seen by reflecting the graph of graph B across the line y = x.
The resulting graph will have no horizontal lines, which means that it passes the horizontal line test, which is a necessary and sufficient condition for a function.
Graph C
The inverse of graph C is a function because for every input value, there is exactly one output value.
This can be seen by reflecting the graph of graph C across the line y = x.
The resulting graph will have no horizontal lines, which means that it passes the horizontal line test, which is a necessary and sufficient condition for a function.