Question

Which statement is true about the given function?

fx) > 0 over the interval (-0,3).
f(x) > 0 over the interval (-:-).
f(x) <0 over the interval (-0,3).
f(x) <0 over the interval (- : -).

Answer 1

Option C.

Explanation:

If the graph of a function f(x) lies above the x-axis, then f(x) > 0.

If the graph of a function f(x) lies below the x-axis, then f(x) < 0.

From the given graph it is clear that the graph of f(x) intersect the x-axis at x=3.

Before x=3 the graph lies below the x-axis. So,

`f(x) < 0` over the interval
`(-\infty,3)`.

After x=3 the graph lies above the x-axis. So,

`f(x) > 0` over the interval
`(3,\infty)`.

Therefore, the correct option is C.