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Question

Determine the following about each graph: a) is the graph a function? b) is the inverse of the graph a function? c) is the graph a one-to-one function?

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Answer 1

By the vertifal line test,

the first is a function, the second is not.

In the first for some y values there are 3 x values. The inverse is not a function

In the second for each y value there is only 1 x value. The inverse is a function

Answer 2

So Kacim L.,

The definition of "function" is that, for each individual value of x, there is ONLY ONE value of y associated. So the first graph qualifies, but the second does not.

By "the inverse of the graph", I'm assuming that means exchanging the x and y axis labels, and rotating the graph into proper position. (Or, you could reflect across the x=y line). Then, the second graph (as inverted) qualifies, but the first does not.

Functions are by definition one-to-one. But if one-to-one is also required for the inverse function, then neither of these graphs qualifies. That would require a monotonically increasing or decreasing function (which could include individual, isolated points of zero slope). Think about this (sketch if needed) until you see why that is.

--Cheers, --Mr. d.