Question

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Explanation:

Identify the parent function and missing text

The visible text asks: "Over which interval is the graph of the parent absolute value function \(f(x) = |x|\) [increasing/decreasing]?"
Looking at the selected option \((0, \infty)\):
The parent absolute value function \(f(x) = |x|\) decreases on \((-\infty, 0)\) and increases on \((0, \infty)\).
Since the selected option is \((0, \infty)\), the question asks for the interval where the function is increasing.

Analyze the behavior of the parent function

Using the Absolute Value Functions knowledge point

$$ f(x) = |x| =
LATEXBLOCK0
$$

Determine the increasing interval

For \(x > 0\), the slope of \(f(x) = x\) is \(1 > 0\).
Thus, the function is strictly increasing on the interval \((0, \infty)\).

Answer:

• (A) \((-\infty, \infty)\)
• (B) \((-\infty, 0)\)
• (C) \((-6, 0)\)
• (D) \((0, \infty)\) (Correct answer)