Question

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

Answer 1

Answer:

The function is  $f(x)=2x-1$

Step-by-step explanation:

If a function has a zero of $\frac{1}{2}$.

The we can write  $x=\frac{1}{2}$.

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  $f(x)=2x-1$

Answer 2

Answer:

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

Step-by-step 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  $\frac{1}{2}$ , let's think that the result must be $f(x)=0$

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

$4)(\frac{1}{2})=2$, now we subtract 2 from this result

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

$4)(\frac{1}{2})-2=0$, we said that $\frac{1}{2}$, 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 $\frac{1}{2}$ is zero of this function