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Which of the following shaded regions sh...

Which of the following shaded regions shows the graph of the inequality `y le |x - 2|` ?

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The correct Answer is:
To solve the inequality \( y \leq |x - 2| \), we will follow these steps: ### Step 1: Understand the Absolute Value Function The expression \( |x - 2| \) represents the distance of \( x \) from 2 on the number line. This function can be expressed as two separate cases: - If \( x \geq 2 \), then \( |x - 2| = x - 2 \). - If \( x < 2 \), then \( |x - 2| = -(x - 2) = 2 - x \).
To solve the inequality \( y \leq |x - 2| \), we will follow these steps: ### Step 1: Understand the Absolute Value Function The expression \( |x - 2| \) represents the distance of \( x \) from 2 on the number line. This function can be expressed as two separate cases: - If \( x \geq 2 \), then \( |x - 2| = x - 2 \). - If \( x < 2 \), then \( |x - 2| = -(x - 2) = 2 - x \).
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