Library of Function

By: Zakiyah Henry

Quadratic Function

f(x)=x^2

Domain: All Reals

Range: [0, ∞)

Zeros: x=0

Y-Axis Symmetry and Even Function

Not Periodic

Not One-to-One

Cubic Function

f(x)= x^3

Domain: All Reals

Range: All Reals

Zeros: x=0

Origin Symmetry and Odd Function

Not Periodic

Is One-to-One

Absolute Value Function

f(x)=| x |

Domain: All Reals

Range: [0,∞)

Zeros: x=0

Y-Axis Symmetry and Even Function

Not Periodic

Not One-to-One

Sine Function

f(x)= sin x

Domain: All Reals

Range: [-1,1]

Zeros: all integers of π

Origin Symmetry and Odd Function

Periodic, 1pd=2π

Not One-to-One

Cosine Function

f(x)= cos x

Domain: All Reals

Range: [-1,1]

Zeros: multiples of π/2

Y-Axis Symmetry and Even Function

Periodic, 1pd=2π

Not One-to-One

Tangent Function

f(x)= tan x

Domain: all reals except odd multiples of π/2

Range: All Reals

Zeros: multiples of π

Origin Symmetry and Odd Function

Periodic, 1pd=π

Not One-to-One

Secant Function

f(x)= sec x

Domain: All Reals except odd multiples of π/2

Range: (-∞,-1] ∪ [-1,∞)

No Zeros

Y-Axis Symmetry and Even Function

Periodic, 1 pd= 2π

Not One-to-One

Exponential Function

f(x)= 2^x

Domain: All Reals

Range: (0,∞)

No Zeros

No Symmetry & Not Even or Odd

Not Periodic

Is One-to-One

Logarithmic Function

f(x)= log2(x)   [2 is a subscript]

Domain: (0,∞)

Range: All Reals

Zeros: x=1

No Symmetry & Not Even or Odd

Not Periodic

Is One-to-One

Rational Function

f(x)= 1/x

Domain: x≠0

Range: y≠0

No Zeros

Origin Symmetry and Odd Function

Not Periodic

Is One-to-One

Square Root Function

f(x)= √x

Domain: x ≥ 0

Range: [0,∞)

Zeros: x=0

No Symmetry & Not Even or Odd

Not Periodic

Is One-to-One

Semi-Circle Function

f(x)= √(a^2-x^2)

Domain: [-a,a]

Range: [0,a]

Zeros: x=-a or a

Y-Axis Symmetry and Even Function

Not Periodic

Not One-to-One

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