To graph the function $$f(x) = -\sqrt{x}$$, we choose non-negative $$x$$-values since the domain of the square root function is restricted to non-negative real numbers. Selecting perfect squares simplifies the calculations. For instance, evaluating the function at $$x$$-values of $$0$$, $$1$$, $$4$$, and $$9$$ yields the $$y$$-values $$0$$, $$-1$$, $$-2$$, and $$-3$$. We then plot the ordered pairs $$(0, 0)$$, $$(1, -1)$$, $$(4, -2)$$, and $$(9, -3)$$ and connect them to sketch the curve.

Claude

To graph the square root function $$f(x) = \sqrt{x}$$, select non-negative $$x$$-values to substitute into the equation to consistently deduce the corresponding $$y$$-values. It is deeply helpful to intentionally choose perfect squares to make calculations easier. For example, selecting the $$x$$-values $$0$$, $$1$$, $$4$$, and $$9$$ produces the corresponding results of $$0$$, $$1$$, $$2$$, and $$3$$, successfully generating the ordered pairs $$(0, 0)$$, $$(1, 1)$$, $$(4, 2)$$, and $$(9, 3)$$. Plotting these coordinates and gracefully connecting them inherently forms a continuous curve that strictly begins at the origin and extends outward to the right.

Example: Graphing the Function $$f(x) = \sqrt{x}$$

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