Question

the square root function
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which statement is true about the function f(x)=√x?
the domain of the graph is all real numbers.
the range of the graph is all real numbers.
the domain of the graph is all real numbers less than or equal to 0.
the range of the graph is all real numbers greater than or equal to 0.
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Explanation:

To determine the true statement about \( f(x)=\sqrt{x} \):

1. Domain of \( \sqrt{x} \): The square root of a negative number is not a real number. So, \( x \geq 0 \) (domain is all real numbers greater than or equal to 0). This eliminates options about domain being all real numbers or \( \leq 0 \).
2. Range of \( \sqrt{x} \): The square root of a non - negative number \( x \) (since \( x\geq0 \)) is also non - negative. For example, \( \sqrt{0} = 0 \), \( \sqrt{4}=2 \), \( \sqrt{9} = 3 \), etc. So the range (output values of \( f(x) \)) is all real numbers greater than or equal to 0.

Answer:

The range of the graph is all real numbers greater than or equal to 0.