# Library of Functions!

### The key to every math problem!

Square Function (y=x^2)

Domain: All Reals

Range: Greater than or equal to zero

Zeros: (0,0)

Symmetry: Y-Axis

Even or Odd?: Even

Periodic?: No

One-One?: No

Here is the graph...

The Cube Function (y=x^3)

Domain: All Reals

Range: All Reals

Zeros: (0,0)

Symmetry: Origin

Even or Odd?: Odd

Periodic?: No

One-One?: Yes

Here is the Graph...

The Absolute Value Function (y=abs(x))

Domain: All Reals

Range: Zero to infinity

Zeros: (0,0)

Symmetry: Y-Axis

Even or Odd?: Even

Periodic?: No

One-One?: No

Here is the Graph...

Sin Function (y=Sin(x))

Domain: All Reals

Range: (-1,1)

Zeros: k(pi) when k is an integer

Symmetry: Origin

Even or Odd?: Odd

Periodic?: yes 2pi

One-One?: No

Here is the Graph...

Cosine Function (y=cos(x))

Domain: All Reals

Range: (-1,1)

Zeros: k(pi) when k is an integer

Symmetry: Y-Axis

Even or Odd?:Even

Periodic?: Yes 2pi

One-One?: No

Here is the Graph...

Tangent Function (y=tan(x))

Domain: Not equal to k*pi/2 and k is odd

Range: All Reals

Zeros: k(pi) when k is an integer

Symmetry: Origin

Even or Odd?: Odd

Periodic?: Yes 2pi

One-One?: No

Here is the Graph...

Secant Function (y=Sec(x))

Domain: Not equal to k*pi/2 and k is odd

Range: (-∞,-1][1,∞)

Zeros: None

Symmetry: Y-Axis

Even or Odd?: Even

Periodic?: Yes 2pi

One-One?: No

Here is the Graph...

Exponential Function (y=2^x)

Domain: All Reals

Range: y>0

Zeros: None

Symmetry: None

Even or Odd?: Neither

Periodic?: No

One-One?: Yes

Here is the Graph...

Logarithm Function

Domain: y<0

Range: All Reals

Zeros: (1,0)

Symmetry: None

Even or Odd?: Neither

Periodic?: No

One-One?: Yes

Here is the Graph...

Rational Function (y=1/x)

Domain: Not equal to 0

Range: Not equal to 0

Zeros: None

Symmetry: Origin

Even or Odd?: Odd

Periodic?: No

One-One?: Yes

Here is the Graph...

Square Root Function (y= sqrt(x))

Domain: [0,∞)

Range: [0,∞)

Zeros: (0,0)

Symmetry: None

Even or Odd?: Neither

Periodic?: No

One-One?: Yes

Here is the Graph...

More Square Root Functions (y=sqrt(a^2-x^2))

Domain: (-a,a)

Range: 0 is less than or equal to Y which is less than or equal to A

Zeros: (-a,a)

Symmetry: Y-Axis

Even or Odd?: Even

Periodic?: No

One-One?: No

Here is the Graph...

And just for fun.....ction

By: Seth Davis