Question

The function varies directly with x and when x = 30.

f(x)
f(x) = 90
What is when x = 6?
f(x)

Answer 1

The function f(x) varies directly with x and f(x) = 90 when x = 30.

f(x)=3x

What is f(x) when x = 6?

f(6)= 3*6 =18

18

Answer 2

`f(6)=18`

In words, the image assigned to
`x=6` is 18.

Explanation:

Givens

• The function varies directly.
• When
  `x=30`,
  `f(x)=90`.

When a function varies directly, it means that function is linear, and it has a direct proportion between variables, so can be modeled by
`f(x)=mx`, where
`m` is the constant ratio of change.

So, in this case, the ratio of change is

`m=(\Delta y)/(\Delta x)=(90)/(30)=3`

That means the linear function that represents this situation is

`f(x)=3x`

So, if
`x=6`, then

`f(x)=3x\\f(6)=3(6)=18`

Therefore,
`f(6)=18`