# 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.