Transformations

Transformation Game 

Compound Interest Formula

Compound Interest: Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan.

P = principal amount (the initial amount you borrow or deposit)

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

n = number of times the interest is compounded per year

Graphing Exponential Equations

Graphing Exponential Growth/Decay

1. Create the Parent Graph.

2. Identify A,H,K.

3. Create your new T-Chart.

• Domain: All real #'s.
• Range: y>k; when a is positive. y<k; when a is negative.
• Asymptote: y=k.

4. Draw Asymptote.

5. Graph new points.

• Exponential Formula: y=a×b^x-h+k
• a = multiplier.

a>1 = stretch
0<a<1 = compression
a< 0(negative) = flipped over x-axis.

• b = base

b>1 = whole #, growth, always increasing.

0<b<1 = fraction; decay, always decreasing.

B is never negative only the multiplier is.

• h = lf/rt; opposite
• k = up/dn

Statistics Test

Statistics Test 

General Forms of a Sequence

A sequence is an ordered list of numbers and the sum of the terms of a sequence is a series

General Form of an Arithmetic Sequence

a_n = a₁ +(n - 1)d

 In an arithmetic sequence, each term is equal to the previous term, plus (or minus) a constant. The constant is called the common difference (d).

General Form of an Geometric Sequence

a_n = a₁·r^n-1

In a geometric sequence, each term is equal to the previous term, multiplied (or divided by) a constant. The constant is called the common ratio.To find the common ratio, divide the second term by the first term

Characteristics and traits

Domain- x-intercepts

Range- y-intercepts 

End behavior- Describing the two ends of a equation 

Absolute Max/min- the one point that is the highest on the graph

Local Max/min- more than one point with a high or low on a graph 

Interval of increase- section of a graph where y values are increasing,describing them in terms in x

Interval of decrease- section of a graph where y values are decreasing 

X-intercept- point where it crosses the x-axis 

Y-intercept- point where it crosses the y-axis 

Symmetry- Even symmetry-symmetric about the y-axis
                     Odd symmetry-symmetric about around origin
                     Neither-no symmetry 

Function-Passes vertical line test 

One to one- passes vertical line test and horizontal line test