Question

Determine whether the formula describes y as a function of x. Why?
y = 9x + 1

Answer 1

My FLVS teacher helped me better my answer:

It is a function because its graph passed the VIRTUAL LINE Test, which demonstrates a function definition that each x value results in only one y value.

Hope that helped :-).

Answer 2

Answer with explanation:

The given function in two variable , x and y ,is

  y = 9 x +1

To check whether it is a function or not, we will check whether it is one-one and onto or not.

A function is said to be one - one,

If,→ f(a) = f(b)

then, a = b

f(a)= 9 a + 1

f(b)= 9 b + 1

→9 a + 1 = 9 b + 1

→ 9 a = 9 b⇒⇒Cancelling , 1 from both sides

→ a =b→Dividing by , 9 on both sides

So, it is one -one.

To check whether , the function is onto or not, if

f(y)=x,then , for every y, there should be unique x or for every x, there is unique y.

y= 9 x +1

9 x= y -1

$x=\frac{y-1}{9}$

For, every ,y there is unique , x.So, this function is onto.

Hence the formula to check the whether, y=9 x +1, is a function or not,

1. Check whether , it is both, one-one and onto.