Question

Which of the following rules represents the function shown in the table?

Answer 1

Answer:

The rule which represent the function as shown in the table is:

                 $f(n)=3n$

Step-by-step explanation:

We are given a table as follows:

  x       2          -1         0

  y       6          -3         0

Now we are asked to find the function which represent these table of values.

a)

    $f(n)=n+3$

Here x is represented by n and y by f(n)

when n=2 we must have f(n)=6

Hence, we put n=2 in the given expression and check,

$f(2)=2+3=5\neq 6$

Hence, this is not a correct function.

b)

$f(n)=\dfrac{1}{3}n$

Again we check for n=2

We have:

$f(2)=\dfrac{1}{3}\times 2=\dfrac{2}{3}\neq 6$

Hence, it is not a correct expression.

So we are left with option: c)

c)

$f(n)=3n$

By putting the value of n=2,-1 and 0

we see that the expression matches the table of values.

( since,

when n=2 we have:

$f(2)=3\times 2=6$

when n= -1 we have:

$f(-1)=3\times -1=-3$

and when n=0 we have:

$f(0)=3\times 0=0$ )

Hence, this is a correct expression.

Answer 2

This is F(n) = 3n

The X is an interger which is holding a value

The relationship between Y and X is 3n as we multiply X by 3 to get the value of Y and is proven yet so.