Question

ntifying the key features of a function from its graph
what intervals would you use to determine where the function is positive and negative?
$(-\infty, -2), (-2, 0), (0, 4),$ and $(4, \infty )$
$(-\infty, \infty)$
$(-\infty, -2), (-2, 4),$ and $(4, \infty)$
$(-2, 4)$

Explanation:

Step1: Identify x - intercepts

The graph of the function intersects the x - axis at $x=-2$ and $x = 4$. These points are the zeros of the function, and we use them to divide the real number line into intervals.

Step2: Determine the intervals

The intervals are determined by the x - intercepts. The real number line is divided into intervals separated by the zeros of the function. So the intervals are $(-\infty,-2)$, $(-2,4)$ and $(4,\infty)$ because the function crosses the x - axis at $x=-2$ and $x = 4$, and we consider the regions between these points and the regions outside the outermost points.

Answer:

$(-\infty, -2)$, $(-2, 4)$, and $(4, \infty )$