19 Basic Functions

y = 1/x

Domain: (-∞,0)∪(0,∞) Range: (-∞, 0)∪(0,∞) Symmetry: Origin Even/odd?: Odd Roots: None

y = 1/(x²)

Domain: (-∞,0)∪(0,∞) Range: (0,∞) Symmetry: Y-axis Even/odd?: Even Roots: None

y = x^1/3

Domain: (-∞,∞) Range: (-∞,∞) Symmetry: Origin Even/odd?: Even Roots: x=0

y = x³

Domain: (-∞,∞) Range: (-∞,∞) Symmetry: Origin Even/odd?: Odd Roots: x=0

y=x

Domain: (-∞,∞) Range: (-∞,∞) Symmetry: Origin Even/odd?: Odd Roots: x=0

y = e^x

Domain: (-∞,∞) Range: (0,∞) Symmetry: None Even/odd?: None Roots: None

y = sin(x)

Domain: (-∞,∞) Range: [-1,1] Symmetry: Origin Even/odd?: Odd Roots: x= ...,-π, 0, π,...

y = cos(x)

Domain: (-∞,∞) Range: [-1,1] Symmetry: Y-axis Even/odd?: Even Roots: x= ...,-π/2, 0, π/2,...

y = x^2/3

Domain: (-∞,∞) Range: [0,∞) Symmetry: Y-axis Even/odd?: Even Roots: x=0

y = |x|

Domain: (-∞,∞) Range: [0,∞) Symmetry: Y-axis Even/odd?: Even Roots: x=0

y=x²

Domain: (-∞,∞) Range: [0,∞) Symmetry: Y-axis Even/odd?: Even Roots: x=0

y = [x]

Domain: (-∞,∞) Range: where y is an integer Symmetry: None Even/odd?: None Roots: Every number between 0 and 1 exclusive and 0

y = ln(x)

Domain: (0,∞) Range: (-∞,∞) Symmetry: None Even/odd?: None Roots: x=1

y = csc(x)

Domain: All real numbers except nπ Range: (-∞,1]∪[1,∞) Symmetry: Origin Even/odd?: Odd Roots: None

y = sec(x)

Domain: All real numbers except nπ + π/2 Range: (-∞,1]∪[1,∞) Symmetry: Y-axis Even/odd?: Even Roots: None

y = tan(x)

Domain: All real numbers except π/2 + πn Range: (-∞,∞) Symmetry: Origin Even/odd?: Odd Roots: x= ...,-π, 0, π,...

y = cot(x)

Domain: All real numbers except πn Range: (-∞,∞) Symmetry: Origin Even/odd?: Odd Roots: x= ...,-π/2, 0, π/2,...

y = sqrt(r² - x²)

Domain: [-r,r] Range: [0,r] Symmetry: Y-axis Even/odd?: Even Roots: x=-r x=r

y = √(x)

Domain: [0,∞) Range:[0,∞) Symmetry: None Even/odd?: None Roots: x=0