Let's analyze the function [tex]\( f(x) = \sqrt{x} \)[/tex] in order to determine its domain and range.
Domain:
1. The domain of a function is the set of all possible input values (x-values) for which the function is defined.
2. The square root function [tex]\( \sqrt{x} \)[/tex] is defined only when the expression inside the square root is non-negative. In other words, [tex]\( \sqrt{x} \)[/tex] exists for [tex]\( x \geq 0 \)[/tex], and it does not exist for [tex]\( x < 0 \)[/tex].
Therefore, the domain of the function [tex]\( f(x) = \sqrt{x} \)[/tex] is all real numbers greater than or equal to 0. This can be written in interval notation as [tex]\([0, \infty)\)[/tex].
Range:
1. The range of a function is the set of all possible output values (y-values) that the function can produce.
2. For the function [tex]\( f(x) = \sqrt{x} \)[/tex], we see that when [tex]\( x = 0 \)[/tex], [tex]\( f(0) = \sqrt{0} = 0 \)[/tex].
3. As [tex]\( x \)[/tex] increases from 0 to positive infinity, [tex]\( \sqrt{x} \)[/tex] also increases from 0 to positive infinity. There is no upper limit on the values that [tex]\( \sqrt{x} \)[/tex] can take for [tex]\( x \geq 0 \)[/tex].
Therefore, the range of the function [tex]\( f(x) = \sqrt{x} \)[/tex] is all real numbers greater than or equal to 0. This can be written in interval notation as [tex]\([0, \infty)\)[/tex].
Summary:
- The domain of [tex]\( f(x) = \sqrt{x} \)[/tex] is all real numbers greater than or equal to 0.
- The range of [tex]\( f(x) = \sqrt{x} \)[/tex] is all real numbers greater than or equal to 0.
Given these observations, the correct statement is:
- The range of the graph is all real numbers greater than or equal to 0.
