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Graphs of three functions are shown below in two or more sentences explain whether or not the inverse of each graph is a function . A. B. C. 

Graph A is \|/
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Graphs of three functions are shown below in two or more sentences explain whether-example-1
User Belogix
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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.

User Lukas Eder
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