Determine X Values for Which f(x) > 0 Using a Graph

Question

Based on the data in the diagram, find for which X values the graph of the function f\left(x\right) > 0

XXXYYY-3-3-3333000

Step-by-Step Solution

First, we examine the provided graph of the quadratic function f(x) f(x) . The graph clearly shows the x-intercepts (where the function crosses the x-axis) at x=3 x = -3 and x=3 x = 3 .

Since the quadratic function appears to be a standard parabola opening upwards, the portion of the graph between these two x-intercepts will be above the x-axis, which means that f(x)>0 f(x) > 0 in this interval.

The intervals to the left of x=3 x = -3 and to the right of x=3 x = 3 will be where the graph lies below the x-axis, meaning f(x)<0 f(x) < 0 in those regions.

Thus, the graph shows that the function f(x) f(x) is positive between x=3 x = -3 and x=3 x = 3 . Therefore, the solution to the problem is:

3<x<3 -3 < x < 3

Answer

-3 < x < 3