Question

Write a function rule for the statement.

1.)the output is half of the input.
2.)the output is one more than twice the input.
3.)the output is the cube if the input.
4.)the output is six times the input

Answer 1

1)

`f(x)=(x)/(2)`

2)

`f(x)=2x+1`

3)

`f(x)=x^3`

4)

`f(x)=6x`

Explanation:

We have to write the function rule for the following statements:

Let 'x' be the input and f(x) represent the output value.

1)

The output is half of the input.

`f(x)=(x)/(2)`

2)

The output is one more than twice the input.

the function in this case is given as firstly we will take two times of the input and then add one to it to obtain the output.

i.e.
`f(x)=2x+1`

3)

The output is the cube if the input.

i.e. the function is given as:

`f(x)=x^3`

4)

The output is six times the input.

i.e. we have to multiply the input by 6.

i.e.
`f(x)=6x`

Answer 2

The correct answers are:
1) f(x)=1/2x;
2) f(x)=2x+1;
3) f(x)=x^3;
4) f(x)=6x.

Explanation:
Let x be the input. In function notation, the output is denoted by f(x).

For #1, since the output is half of the input, we want to take half of x; this would give us
f (x)=
`(1)/(2)`x.

For #2, twice the input is 2x; one more than this is 2x+1, which gives us
f (x)=2x+1.

For #3, the cube of the input is x³, which gives us
f (x)=x³.

For #4, six times the input is 6x, which gives us
f (x)=6x.