Question

13. Write a function with a zero of 1/2. Explain how you know.

Answer 1

The function is
`f(x)=4x-2`

Explanation:

That a function has a zero at a certain number x means that
`f(x)=0`

Let's see an example,

If we have
`f(x)=x+2` (this is what we call function)

and we choose any value for the x,

x = 3

Now we replace it in our function

`f(3)=3+2`

`f(3)=5` (this is the image of 3)

Now if we say that x = -2, and replace it in our function

`f(-2)=(-2)+2`

`f(-2)=0` , this means that our function has a zero at x = -2

We can find the zeros of our function equaling it to zero and clearing the x, let's see

`x+2=0`

`x=-2` this means that our function has a zero at x = -2

To find a function that has a zero at
`(1)/(2)` , let's think that the result must be
`f(x)=0`

If we have 4 and multiply it by 1/2.

`4)((1)/(2))=2`, now we subtract 2 from this result

`-2 = 0` , the complete process would be

`4)((1)/(2))-2=0`, we said that
`(1)/(2)`, then

`4x-2`, now we write it as a function

`f(x)=4(x)-2` we know that by replacing the x by 1/2 the result will be zero, which means that
`(1)/(2)` is zero of this function

Answer 2

The function is
`f(x)=2x-1`

Explanation:

If a function has a zero of
`(1)/(2)`.

The we can write
`x=(1)/(2)`.

We need to work backwards to obtain the function:

We multiply through by 2 to get:

`2x=1`.

This implies that:

`2x-1=0`

Hence a function with such zero is
`f(x)=2x-1`