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A Function. That is the definition of a function.
I like to think of a function, f(x) as a number crunching machine. the number crunching machine eats different x 's. It eats each and every x and crunches it the same way, but spits out a new Y every time. Remember, y = f(x). That is, "y is a function of x".
There you go.
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What is a relation in which each x-value has one and only one y-value?
It is a surjective relationship. It may or may not be injective, and therefore, bijective.
What inverse relation means?
Two variables, X and Y, are in inverse relation if X*Y = a constant.
Is the relation (-1 4) (2 7) (37) a function?
Yes, there is only one y value for each x value.
What is it called if any vertical line crosses the graph of a relation more than once the relation is not a function?
The Vertical Line Test An example might be x=cos(y). At any value of x between -1 a nd +1 (a vertical line on the graph) this is multivalued (and so it is called "multivalued"). The relation is a function, because given y you can calculate x. x is a function of y. The relation between y and x can also be written y=cos-1(x) "y is the angle whose cosine is x". From that point of view you can say " y is not a function of x" because for each x, there is more than one y that satisfyies the equation. To summarize, in this example x is a function of y but y is not a function of x.
What are different shapes of functions and relations?
A relation is just a set of ordered pairs. They are in no special order. Therefore there is no particular shape assigned to a relation. A function is a special kind of relation. A relation becomes a function when the x value only has one y value.
