The range of the function $f (x) = - | x - 2 | - 3$ is

y \geq 2

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y \leq - 3

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y \geq - 3

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y \leq - 2

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y \geq - 2

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Solution

The correct option is B $y \leq - 3$
Given, $f (x) = - | x - 2 | - 3$
We know that modulus is always greater than or equal to zero, so we have $| x - 2 | \geq 0$ , which implies $- | x - 2 | \leq 0$ .
Therefore $- | x - 2 | - 3 \leq - 3$ , which implies $y \leq - 3$

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