Vertex of an Absolute Value Function

In technical quality control and data analysis, the absolute value function is used to model the deviation of a measurement from a target value. Match each property of the parent absolute value function, $f(x) = |x|$, with its correct mathematical description.

In a laboratory setting, a scientist uses the parent absolute value function $f(x) = |x|$ to report the magnitude of temperature fluctuations in a freezer. Based on the definition of this function, which of the following intervals represents its range?

Geometric Properties of the Absolute Value Function

In a laboratory setting, a technician uses the parent absolute value function $f(x) = |x|$ to record the magnitude of temperature variations. Because this function can accept any value on the number line as an input, its domain is the set of all ____ numbers.

In professional quality control, the absolute value function $f(x) = |x|$ is used to calculate the magnitude of measurement errors. True or False: The range of this parent function is strictly restricted to non-negative real numbers, [0, infty), because the absolute value of a number represents its physical distance from zero.

Recall of Absolute Value Graph Properties in Manufacturing Quality Control

In a precision manufacturing facility, a Quality Control (QC) inspector is verifying the dimensions of a critical machine component. The target width of the component is ${}50\text{ mm}$. Any variation from this target is modeled using the parent absolute value function, where the input $x$ represents the raw deviation from the target width, and the output represents the magnitude of the error. To document this process on the quality control chart, the inspector needs to recall the key characteristics of the parent absolute value function $f(x) = |x|$ to model the error graph. Arrange the following steps in the correct logical sequence to construct the absolute value error graph from left to right (from $x \to -\infty$ to $x \to \infty$).