Question

Which relations represent functions

Answer 1

Definition of a function: A function is a special relationship where each input has a single output.

1. Here for all x there exist only one y such that f(x)=y. That's why this is function.
2. Here f(x)=5 and f(x)=7 (for one x there are two y). This relation doesn't represent a function.
3. Here for all x there exist only one y such that f(x)=y. That's why this is function.
4. Here f(a)=55 and f(a)=25 (for one x there are two y). This relation doesn't represent a function.

Answer 2

Figure 1 and 3 represent functions

Further explanation

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y

A function can be expressed in the form of a cartesian diagram, sequential pairs, or arrow diagram

If a function (f) pairs members of set A to set B, then the inverse of function f (f-1) pairs members of set B to A, or easily f-1 is the opposite of f

or in the form of equations

f (x) = y if and only if g (y) = x

g (y) is called the inverse of f (x)

We see the options available

From the pictures, we can set A and B

• 1

A = {- 1,0,1,5,7}

B = {-2,4,3,14}

Each member A is paired exactly one with member B, so that it is a function

• 2

A = {x, y}

B = {7,3,5}

There is one member A that is paired with 2 members B, namely (x.5) and (x.7) so that it is not a function

• 3

A = {John, Ted}

B = {52}

Each member A is paired exactly one with member B, so that it is a function

• 4

A = {a, b, c, d}

B = {25,35,45,55}

There is one member A that is paired with 2 members B, namely (a, 25) and (a, 55) so that it is not a function

Learn more

the function has an inverse function

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the inverse of the function

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