Does the graph represent a function that has an inverse func

Does the graph represent a function that has an inverse function?

Solution

Remember that only one-­to-­one function have an inverse.

In looking at the graph of the function we can determine if a function is a one-­to-­one function or not by applying the Horizontal Line Test, or HLT.

Horizontal Line Test – The HLT says that a function is a one­-to­-one function if there is no horizontal line that intersects the graph of the function at more than one point.

If the graph of the function passes the Horizontal Line Test, then the function is a one­to­one function. If the graph of the function fails the Horizontal Line Test, then the function is not a one­to­one function. By applying the Horizontal Line Test not only can we determine if a function is a one­to­one function, but more importantly we can determine if a function has an inverse or not

A one­to­one function is special because only one­to­one functions have an inverse function

In looking at the graph, you can see that any horizontal line drawn on the graph intersects the graph more than once.

Take for example x-axis itself which is a horizontal line which cuts the graph at two points i,e more than one.

Therefore,This function does not pass the Horizontal Line Test which means it is not a one­to­one function and does not have an inverse.

Thus, the given graph does not represent a function that has an inverse function.

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