Algebra 2 Chapter 7 Test Flashcards

Characteristics of Exponential Growth Function

• Continuous function with a domain of all real numbers.
• Range consists of positive numbers only.
• The asymptote is the x-axis.

Transformation of Exponential Function Equation

• General form: (F(x) = ab^{x-h} + k).
• Parameters (h) and (k) enable shifting the graph horizontally and vertically.

Parameter H

• Controls horizontal movement along the x-axis.
• Shifts the function in the opposite direction of its value.

Parameter K

• Governs vertical translation on the y-axis.
• Moves the graph up or down depending on its value.

Parameter A

• Defines the orientation and shape of the exponential graph.
• If (0 < |a| < 1), the function is vertically stretched.

Characteristics of Exponential Decay Function

• Also a continuous function with a domain of all real numbers.
• The range is positive numbers with an asymptote on the x-axis.

Exponential Decay Equation

• Formulated as (Y = a(1-r)^t) for decay scenarios.

Exponential Growth Function

• Expressed as (Y = a(1+r)^t), indicating growth over time.

Solving Exponential Equations

• Use a common base for both sides before ignoring the base to solve the equation.

Logarithm

• Defined as (Y = \log_b x) with (b > 0) and (b \neq 1).
• Functions as the inverse of exponential functions.

Property of Equality for Logarithmic Functions

• If (b) is a positive number (and not 1), then ( \log_b x = \log_b y) holds true if and only if (x = y).

Product Property of Logarithms

• The logarithm of a product is calculated as the sum of the logarithms of each factor: ( \log_b(xy) = \log_b x + \log_b y ).

Quotient Property of Logarithms

• The logarithm of a quotient is represented as the difference of the logarithms: ( \log_b(x/y) = \log_b x - \log_b y ).

Power Property of Logarithms

• The logarithm of a power is equal to the product of the logarithm and its exponent: ( \log_b(x^n) = n \cdot \log_b x ).

Common Logs

• Logs that have a base of 10, denoted simply as ( \log x ).

Change of Base Formula

• Enables the conversion of logarithms from one base to another: ( \log_a b = \frac{\log_n b}{\log_n a} ).

Compound Equation

• Represents the formula for compound interest: (A = P(1 + \frac{r}{n})^{nt}).

Transformation of Logarithmic Function Equation

• Formulated as (A \log_b (x-h) + k), allowing for horizontal and vertical shifts.