Question

Write the function rule.

(a) The ouput is five less than the input.
(b) The output is one fourth the input.
(c) The ouput is one more than twice the input.

Answer 1

Let x represent input and y represent output.

We are asked to write function rule for each of the given verbal description.

(a) The output is five less than the input.

This means that y is 5 less than x. So we will subtract 5 from x and equate with y as:

`y=x-5`

Therefore, our required expression would be
`y=x-5`.

(b) The output is one fourth the input.

This means that y is
`(1)/(4)` of x. So we will multiply x by
`(1)/(4)` and equate with y as:

`y=(1)/(4)x`

Therefore, our required expression would be
`y=(1)/(4)x`.

(c) The output is one more than twice the input.

The twice of the input would be 2 times x that is
`2x`.

One more than twice the input would be
`2x` plus 1 that is
`2x+1`.

Now we will equate
`2x+1` with y as:

`y=2x+1`

Therefore, our required expression would be
`y=2x+1`.