General Forms of a Sequence

Arithmetic and Geometric Sequences

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Arithmetic Sequence: a_n= a₁ + (n-1)d

a₁=first term

                                    d=difference

                             a_n=undefined variable

 

Geometric: a_n= a₁ • r^n-1

Characteristics and Traits

Characteristics and Traits

Domain: left to right

Range: up to down

 

End Behavior:

· Left: X → -∞

o Y → +∞ (up)

o Y → - ∞ (down)

· Right: X → + ∞

o Y → +∞ (up)

o Y → - ∞ (down)

Function: passes vertical line test

Once to One: passes vertical and horizontal line test

X-Intercept= (a, 0)

Y-Intercept= (0,b)
 

Absolute Max/Min= one max/min point

Local Max/Min= two max/min point

Symmetry:

· Even- symmetric about Y-Axis

· Odd- rotational symmetry about origin

· Neither- none

Interval of increase: whether line goes up or down on X-Axis

Interval of Decrease: whether line goes left or right on X-Axis

Intercepts: where the lines passes the Y or X axis

Asymptotes: imaginary line that a graph gets closer and closer to but never touches