Question

which statement is true about the graphed function \\(f(x)\\)?

\\(f(x) < 0\\) over the intervals \\((-\infty, -2.5)\\) and \\((-0.75, 0.75)\\).
\\(f(x) > 0\\) over the intervals \\((-\infty, -2.5)\\) and \\((-0.75, 0.75)\\).
\\(f(x) < 0\\) over the intervals \\((-2.5, -0.75)\\) and \\((-0.75, \infty)\\).
\\(f(x) > 0\\) over the intervals \\((-2.5, -0.75)\\) and \\((0.75, \infty)\\).

Explanation:

Identify the x-intercepts

Using the Function Graph Analysis knowledge point

$$ \text{The graph of } f(x) \text{ crosses the } x\text{-axis at } x = -2.5, \quad x = -0.75, \quad \text{and} \quad x = 0.75. $$

Determine the sign of the function

Using the Function Graph Analysis knowledge point

$$
LATEXBLOCK0
$$

Match with the given options

Using the Function Graph Analysis knowledge point

$$ \text{The statement } "f(x) > 0 \text{ over the intervals } (-\infty, -2.5) \text{ and } (-0.75, 0.75)" \text{ is true.} $$

Answer:

• O \(F(x) < 0\) over the intervals \((-\infty, -2.5)\) and \((-0.75, 0.75)\).
• O \(F(x) > 0\) over the intervals \((-\infty, -2.5)\) and \((-0.75, 0.75)\). (Correct answer)
• O \(F(x) < 0\) over the intervals \((-2.5, -0.75)\) and \((-0.75, \infty)\).
• O \(F(x) > 0\) over the intervals \((-2.5, -0.75)\) and \((0.75, \infty)\).