Answer:
[tex]f(x)<0[/tex] on the interval [tex]0<x[/tex]
[tex]f(x)<0[/tex] on the interval [tex]0<x<1[/tex]
[tex]f(x)>0[/tex] on the interval [tex]1<x<3[/tex]
[tex]f(x)<0[/tex] on the interval [tex]x>3[/tex]
Step-by-step explanation:
Remember that [tex]f(x)=y[/tex]. When the graph of the function is below the x-axis, the value of [tex]y[/tex] is negative; therefore the function is less than zero, or in math notation: [tex]f(x)<0[/tex]. On the other hand, when the graph of the function is above the x-axis, the value of [tex]y[/tex] is positive; therefore, the function is grater than zero, or in math notation: [tex]f(x)>0[/tex].
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:
[tex]f(x)<0[/tex] on the interval [tex]x<1[/tex] and [tex]f(x)<0[/tex] on the interval [tex]x>3[/tex]
We can also infer from our graph that our function is above the x-axis from 1 to 3, so:
[tex]f(x)>0[/tex] on the interval [tex]1<x<3[/tex]
Knowing this we can conclude that the true statements are:
[tex]f(x)<0[/tex] on the interval [tex]0<x[/tex]
[tex]f(x)<0[/tex] on the interval [tex]0<x<1[/tex]
[tex]f(x)>0[/tex] on the interval [tex]1<x<3[/tex]
[tex]f(x)<0[/tex] on the interval [tex]x>3[/tex]
