Let's analyze the functions \( f(x) = -\sqrt{x} \) and \( g(x) = -\sqrt[3]{x} \).
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Domains:
- For \( f(x) = -\sqrt{x} \): The square root function is defined for \( x \geq 0 \). Therefore, the domain of \( f(x) \) is \( [0, \infty) \).
- For \( g(x) = -\sqrt[3]{x} \): The cube root function is defined for all \( x \). Thus, the domain of \( g(x) \) is \( (-\infty, \infty) \).
- Conclusion: The graphs do not have the same domain.
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Ranges:
- For \( f(x) = -\sqrt{x} \): The range is all non-positive real numbers since as \( x \) approaches \( 0 \), \( f(x) \) approaches \( 0 \) and goes to \( -\infty \) as \( x \) increases. So the range is \( (-\infty, 0] \).
- For \( g(x) = -\sqrt[3]{x} \): The range is also all real numbers since the cube root function can take any value. Therefore, multiplying by -1 gives \( (-\infty, \infty) \).
- Conclusion: The graphs do not have the same range.
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Monotonicity (Increasing/Decreasing):
- For \( f(x) = -\sqrt{x} \): This function is decreasing on its domain \( [0, \infty) \) because as \( x \) increases, \( -\sqrt{x} \) decreases.
- For \( g(x) = -\sqrt[3]{x} \): This function is also decreasing for all real \( x \) since as \( x \) increases, \( -\sqrt[3]{x} \) also decreases.
- Conclusion: Both graphs are decreasing.
Based on the analysis, the true statements are:
- The graphs have the same ranges. (False)
- The graphs have the same domains. (False)
- The graphs are both increasing. (False)
- The graphs are both decreasing. (True)
Final Answer: The graphs are both decreasing.