Introduction to Absolute Value Functions (HSC SSCE Mathematics Advanced): Flashcards

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Introduction to Absolute Value Functions
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Absolute value represents

Distance of a number from zero on a number line

Sign of absolute value output

Always non-negative

Notation for absolute value function

f(x)=∣x∣f(x) = |x|

Piecewise definition of ∣x∣|x|

xx if x≥0x \geq 0; −x-x if x<0x < 0

Domain of f(x)=∣x∣f(x) = |x|

All real numbers, (−∞,∞)(-\infty, \infty)

Range of f(x)=∣x∣f(x) = |x|

All non-negative real numbers, [0,∞)[0, \infty)

Graph shape of y=∣x∣y = |x|

V-shaped curve

Vertex of y=∣x∣y = |x| graph

(0,0)(0, 0)

Symmetry of y=∣x∣y = |x| graph

Symmetric about the y-axis

Identity: x2\sqrt{x^2} equals

∣x∣|x|

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