3. \( f(x)=|x|-3 \)

This absolute value function, \( f(x) = |x| - 3 \), represents a V-shaped graph that is shifted down by 3 units from the parent function \( f(x) = |x| \). The vertex of this graph is at the point \( (0, -3) \). This characteristic means that for any input \( x \), the output will never be less than -3, showcasing the elegant way absolute values create boundaries in functions! In real-world terms, this function can model various scenarios, such as calculating the elevation of a location relative to sea level. If sea level is treated as 0, \( f(x) \) reveals how far above (for positive \( x \)) or below (for negative \( x \)) sea level you are, establishing a straightforward way to visualize geographical features or structural heights!