To graph the function $$f(x) = -|x|$$, we select a range of $$x$$-values to determine their corresponding $$y$$-values. Substituting $$x$$-values such as $$-3$$, $$-2$$, $$-1$$, $$0$$, $$1$$, $$2$$, and $$3$$ into the function yields the $$y$$-values $$-3$$, $$-2$$, $$-1$$, $$0$$, $$-1$$, $$-2$$, and $$-3$$. Plotting these ordered pairs on a coordinate plane and connecting them produces a downward-opening V-shaped graph.

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To actively graph the absolute value function $$f(x) = |x|$$, purposefully select a range of both positive and negative $$x$$-values to substitute into the equation. For instance, directly evaluating the integers from $$-3$$ to $$3$$ yields the corresponding ordered pairs $$(-3, 3)$$, $$(-2, 2)$$, $$(-1, 1)$$, $$(0, 0)$$, $$(1, 1)$$, $$(2, 2)$$, and $$(3, 3)$$. Plotting these specific coordinates on a geometric graph and connecting the successive points definitively reveals a symmetrical V-shaped graph possessing its vertex purely at the origin $$(0, 0)$$, physically demonstrating that all corresponding output values are non-negative.

Example: Graphing the Function $$f(x) = |x|$$

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