Question

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e absolute value function, f(x) = x + 21, is shown.
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TIME REMAININ
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If the graph is reflected over the x-axis, what is the
domain of the function?
O all real numbers
O all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
O all real numbers less than or equal to -2

Answer 1

The correct option is "The domain remains unchanged, comprising all real numbers."

When the graph of the absolute value function
`\(f(x) = x + 2\)` is reflected over the x-axis, the transformation does not affect the domain. The domain represents all possible x-values, and reflection over the x-axis preserves this set of values.

Therefore, the correct answer is:

a) The domain remains unchanged, comprising all real numbers.

Reflecting the graph over the x-axis changes the sign of the y-values but does not alter the set of possible x-values. The absolute value function, whether reflected or not, maintains its domain of all real numbers. This is a fundamental characteristic of such functions, and transformations that involve reflection across the x-axis do not impact the domain.