# Library of Functions

where we put the FUN in FUNction

# Square Function

Domain: ALL REALS

Range: y ≥ 0

Zeros: x = 0

Symmetry: Even

Periodic: No

One - to - One: No

Graph:

# Cubic Function

Domain: ALL REALS

Range: ALL REALS

Zeros: x = 0

Symmetry: odd

Periodic: No

One - to - One: Yes

Graph:

# Absolute Value Function

Domain: ALL REALS

Range: y ≥ 0

Zeros: x = 0

Symmetry: Even

Periodic: No

One - to - One: No

Graph:

# Sine Function

Domain: ALL REALS

Range: [-1,1]

Zeros: Multiples of Pi

Symmetry: Odd

Periodic: Yes, 2Pi

One - to - One: No.

Graph:

# Cosine Function

Domain: ALL REALS

Range: [-1,1]

Zeros: Odd multiples of Pi/2

Symmetry: Even

Periodic: Yes. 2Pi

Graph:

# Tangent Function

Domain: ALL REALS, EXCEPT odd multiples of Pi/2

Range: ALL REALS

Zeros: Multiples of Pi

Symmetry: Odd

Periodic: Yes, 2Pi

One - to - One: No.

Graph:

# Secant Function

Domain: ALL REALS, EXCEPT odd multiples of Pi/2.

Range: Y ≤ -1, y ≥ 1

Zeros: N/A

Symmetry: Even

Periodic: Yes, 2Pi

One - to - One: No

Graph:

# Exponential Function

Domain: ALL REALS

Range: y > 0

Zeros: N/A

Symmetry: N/A

Periodic: No

One - to - One: Yes

Graph:

# Logarithmic Function

Domain: x > o

Range: ALL REALS

Zeros: x = 1

Symmetry: N/A

Periodic: No

One - to - One: Yes

Graph:

# Rational Function

Domain: x ≠ 0

Range: y ≠ 0

Zeros: N/A

Periodoic: No

One - to - One: Yes

Graph:

# Square Root Function

Domain: x ≥ 0

Range: y ≥ 0

Zeros: x = 0

Symmetry: N/A

Periodic: No

One - to - One: Yes

Graph:

Last but most certainly not least... ( I couldn't figure out how to make it a headline too, oops)

Domain: [-a,a]

Range: 0 ≤ Y, Y ≤ a

Zeros: x = ± A

Symmetry: Even

Periodic: No

One - to - One: No

Graph:

# a few little key notes...

- Domain is the set of values that can be X

- Range is the set of values that can be Y

-A "zero" is where the graph crosses the axis

-To have even symmetry, the graph should be symmetrical to the Y-Axis. For the function to be odd, the graph should be symmetrical to the Origin.

-For a function to be periodic, the graph would have to repeat itself in some sort of pattern in a given space.

-For a function to be one to one, it must not only pass the vertical line test, but the horizontal one as well.

# About the Authors

The young authors, Allyson Butler and Joshua "Cole" Hedrick, were instructed by their Calculus teacher to create this page to describe in detail the library of functions. Allyson and Cole have known each other very well throughout their high school careers, sharing a lot of the same interests and hobbies. With their equal struggles in math over the past four years, they created a bond like no other. Math has brought two people together to be friends for a lifetime.