To compare the graphs of the functions \( f(x) = -\sqrt{x} \) and \( g(x) = -\sqrt{3} \), let's analyze their features.
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Domains:
- The function \( f(x) = -\sqrt{x} \) is defined for \( x \geq 0 \) because you cannot take the square root of a negative number. Thus, its domain is \( [0, \infty) \).
- The function \( g(x) = -\sqrt{3} \) is a constant function, which is defined for all \( x \). Hence, its domain is \( (-\infty, \infty) \).
- Therefore, the graphs do not have the same domains.
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Ranges:
- The function \( f(x) = -\sqrt{x} \) outputs values that range from \( 0 \) (when \( x=0 \)) down to \( -\infty \) as \( x \) increases. Thus, its range is \( (-\infty, 0] \).
- The function \( g(x) = -\sqrt{3} \) is constant and its range is simply \( {-\sqrt{3}} \).
- Thus, the graphs do not have the same ranges.
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Increasing/Decreasing Behavior:
- The function \( f(x) = -\sqrt{x} \) is decreasing on its domain \( [0, \infty) \) because as \( x \) increases, \( -\sqrt{x} \) decreases.
- The function \( g(x) = -\sqrt{3} \) is a constant function, which means it neither increases nor decreases.
- Therefore, neither graph is both increasing.
Given this analysis, the correct statement comparing the two graphs is:
The graphs are both decreasing. (The accurate option would actually denote that \( f(x) \) is decreasing and \( g(x) \) is constant, but neither is completely correct as a set.)
Therefore, none of the options provided in the question are true based on the accurate description of the features of the graphs.
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