Question: What is the range of this function?
y = |x|
{y | y \leq 0}
{y | y > 0}
{y | y \geq 0}
{y | y < 0}
Graph shape: the function y = |x| is an upward-opening V-shaped graph with vertex at the origin, so its range is {y | y \geq 0}.
1. **State the problem:** We need to find the range of the function $$y = |x|$$.
2. **Recall the definition:** The absolute value function $$|x|$$ outputs the distance of $$x$$ from zero on the number line, which is always non-negative.
3. **Analyze the function:** Since $$|x| \geq 0$$ for all real numbers $$x$$, the smallest value $$y$$ can take is $$0$$, and it can increase without bound.
4. **Range conclusion:** Therefore, the range of $$y = |x|$$ is all $$y$$ such that $$y \geq 0$$.
5. **Express in set notation:** The range is $$\{ y \mid y \geq 0 \}$$.
**Final answer:** The range of $$y = |x|$$ is $$\{ y \mid y \geq 0 \}$$.