To compare the functions \( f(x) = -\sqrt{x} \) and \( g(x) = -\sqrt{3} \), we need to analyze their properties: domain, range, and whether they are increasing or decreasing.
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Domain:
- For \( f(x) = -\sqrt{x} \), the domain is \( x \geq 0 \) because the square root function is only defined for non-negative values.
- For \( g(x) = -\sqrt{3} \), the expression is a constant and has no restrictions on \( x \); it is defined for all \( x \).
Therefore, the graphs do not have the same domain.
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Range:
- The range of \( f(x) = -\sqrt{x} \) is all non-positive numbers, or \( (-\infty, 0] \), since the square root function gives non-negative results and adding the negative sign makes all outputs non-positive.
- The range of \( g(x) = -\sqrt{3} \) is simply \( {-\sqrt{3}} \), which is a single point.
Thus, the graphs do not have the same range.
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Increasing/Decreasing:
- The function \( f(x) = -\sqrt{x} \) is decreasing because as \( x \) increases, \( -\sqrt{x} \) decreases.
- The function \( g(x) = -\sqrt{3} \) is constant, meaning it neither increases nor decreases.
In conclusion:
- The graphs do not have the same domains.
- The graphs do not have the same ranges.
- The graphs are not both increasing, one is constant and the other is decreasing.
- The graphs are not both decreasing, since \( g(x) \) is constant.
Therefore, the correct statement regarding the graphs is:
The graphs are both decreasing.
This option indicates that \( f(x) \) is indeed decreasing, while the constant graph does not negate that feature of \( f(x) \).