Question

20 POINTS! TTM
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Answer 1

A relation is (also) a function if every input x is mapped to a unique output y.

In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:

1. The first graph is exactly a vertical line, so it's not a function.
2. The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.
3. The third graph is not a function, because you can draw vertical lines that cross the graph twice.
4. Similarly, in the fourth graph you can draw vertical lines that cross the graph twice
5. The fifth graph is a function, because every vertical line crosses the graph once
6. The last graph is a function, although discontinuous, for the same reason.

Answer 2

Answer:

A relation is (also) a function if every input x is mapped to a unique output y.

In terms of graphical representation, this implies that a graph represents a function if there doesn't exist a vertical line that intersects the graph more than once. So:

The first graph is exactly a vertical line, so it's not a function.

The second graph represents the function y=x, so it's a function: you can see that every possible vertical line crosses the graph only once.

The third graph is not a function, because you can draw vertical lines that cross the graph twice.

Similarly, in the fourth graph you can draw vertical lines that cross the graph twice

The fifth graph is a function, because every vertical line crosses the graph once

The last graph is a function, although discontinuous, for the same reason.

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