Question

please help me and explain why

Answer 1

Answer:

{(0, 1), (2, 7), (3, 4), (-4, -1), (-6, 7)}

This diagram represents a function because each value of x corresponds to exactly one value of y.

If you plot these points on the coordinate plane, you will notice that this set of points represents a function because it passes the Vertical Line Test.

Answer 2

Answer:  Yes it's a function.

Reason: Each input maps to exactly one output

In other words, one input ---> one output.

If you were to plot each (x,y) point on the same grid, then you should notice the graph passes the vertical line test. This is where we try to draw a vertical line through multiple points. But such a task is impossible in this case. This is a visual indicator we have a function. See the diagram below.

The (x,y) points are

(0,1), (2,7), (3,4), (-4,1), (-6,7)

Notice how none of the x values repeat themselves. If some of the x values did repeat, then we wouldn't have a function.

The y values can repeat, but the function wouldn't be one-to-one (aka injective).