Absolute Value Function Properties
This Grade 11 math skill from enVision Algebra 1 defines the properties of the absolute value function. The absolute value function f(x) = |x| has a domain of all real numbers (negative infinity to positive infinity) and a range of all non-negative real numbers [0, infinity). Students learn that the absolute value of any number is always zero or positive — it measures distance from zero on the number line. Understanding domain and range for this function prepares students for graphing transformations and piecewise function analysis in Algebra 1.
Key Concepts
| Function | Definition | Domain | Range | | | | | | | Absolute Value Function| $f(x) = \lvert x \rvert$ | $( \infty, \infty)$ | $[0, \infty)$ |.
Common Questions
What is the absolute value function?
The absolute value function f(x) = |x| returns the non-negative distance of x from zero on the number line. For positive numbers or zero it returns x unchanged; for negative numbers it returns -x (making it positive).
What is the domain of the absolute value function?
The domain of f(x) = |x| is all real numbers, written (-∞, ∞). You can input any real number — positive, negative, or zero — into the absolute value function.
What is the range of the absolute value function?
The range of f(x) = |x| is [0, ∞) — all non-negative real numbers. The absolute value function always outputs zero or a positive number, never a negative result.
What does the graph of the absolute value function look like?
The graph of f(x) = |x| is a V-shape with its vertex at the origin (0,0). The left arm has slope -1 and the right arm has slope 1, both extending upward from the vertex.
How is the absolute value function used in Algebra 1?
In Algebra 1, absolute value functions are used to model real-world distance problems, solve absolute value equations and inequalities, and study function transformations including shifts, reflections, and stretches.