Question

Based on the graph of the function which of the following statements are true?

Answer 1

`f(x)<0` on the interval
`0<x`

`f(x)<0` on the interval
`0<x<1`

`f(x)>0` on the interval
`1<x<3`

`f(x)<0` on the interval
`x>3`

Explanation:

Remember that
`f(x)=y`. When the graph of the function is below the x-axis, the value of
`y` is negative; therefore the function is less than zero, or in math notation:
`f(x)<0`. On the other hand, when the graph of the function is above the x-axis, the value of
`y` is positive; therefore, the function is grater than zero, or in math notation:
`f(x)>0`.

We can infer from our graph that our function is bellow the x-axis from minus infinity to minus -1, and form three to infinity. In math notation:

`f(x)<0` on the interval
`x<1` and
`f(x)<0` on the interval
`x>3`

We can also infer from our graph that our function is above the x-axis from 1 to 3, so:

`f(x)>0` on the interval
`1<x<3`

Knowing this we can conclude that the true statements are:

`f(x)<0` on the interval
`0<x`

`f(x)<0` on the interval
`0<x<1`

`f(x)>0` on the interval
`1<x<3`

`f(x)<0` on the interval
`x>3`