The 12 Mother Functions Y=X

D: (-∞,∞)

R: (-∞, ∞)

continuous

Odd

No HA, No VA

Not Bounded Identity Function(linear) Y=sin(X)

D: (-∞,∞)

R:(-1,1)

Continuous

Odd

No VA, No HA

Not Bounded Sine Function Y=1/1+e^-x

d:(-∞,∞)

R: (0,1)

continuous

No symmetry

HA: Y=0, Y=1

VA: none

Bounded Logistic Function Y=e^x

D: (-∞,∞)

R: (0,∞)

continuous

No symmetry

HA: Y=0

VA: none

Bounded below Exponential Function Y=cos(X)

D: (-∞,∞)

R: [-1,1]

continuous

Even

NO HA, No VA

Bounded Cosine Function Y=X^3

D: (-∞,∞)

R: (-∞, ∞)

continuous

Odd

No HA, No VA

Not Bounded Cubing Function (Cubic) Y=1/X

D: (-∞,0);(0,∞)

R: (-∞,0);(0,∞)

discontinuous X=0

Odd

VA: X=0

HA: Y=0

Bounded inbetween Reciprocal Function Y=X^2

D: (-∞,∞)

R: [0, ∞)

continuous

Even

No HA, No VA

Bounded Below Squaring Function(Quadratic) Y=lnX

D: (0,∞)

R: (-∞, ∞)

continuous

No Symmetry

No HA,

VA: X=0

Not Bounded Natural Log Function Y=int(X)

D: (-∞,∞)

R: all integers

Jump discontinuity

No Symmetry

No HA, No VA

Not Bounded Greatest Integer Function Y=|X|

D: (-∞,∞)

R: [0, ∞)

continuous

Even

No HA, No VA

Bounded Below Absolute Value Y=√X

D: [0,∞)

R: [0, ∞)

continuous

No Symmetry

No HA, No VA

Bounded Below Square Root Function

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# The 12 Mother Functions

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