The range of 𝑓(𝑥)=∣𝑥−3∣f(x)=∣x−3∣is:A.None of theseB.𝑦≥3y≥3C.𝑦<3y<3D.𝑦>3y>3E.𝑦≥0y≥0

Break Down the Problem

1. Identify the function: $f(x) = |x - 3|$.
2. Determine the properties of the absolute value function to find its range.

Relevant Concepts

1. The absolute value function $|a|$ is always non-negative, meaning $|x - 3| \geq 0$ for all $x$.
2. The minimum value occurs at $x = 3$, where $f(3) = |3 - 3| = 0$.

Analysis and Detail

1. Since $f(x) = |x - 3|$, the function reaches a minimum of 0 when $x = 3$.
2. As $x$ moves away from 3 in either direction, $f(x)$ increases without bound.

Verify and Summarize

1. The lowest point of the graph is at $y = 0$ (when $x = 3$).
2. There is no upper bound on $y$; hence $f(x)$ can take any value greater than or equal to 0.

Final Answer

The range of $f(x) = |x - 3|$ is $y \geq 0$. Thus, the correct answer is E. $y \geq 0$.