Algebra 2 Chapter 7 Test Flashcards

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Questions and Answers

What are the characteristics of an exponential growth function?

Continuous, domain is all real numbers and range positive numbers. Asymptote is the x-axis.

What is the transformation of the exponential function equation?

F(x) = ab^(x-h) + k

What does 'H' represent in the context of transformations?

Along the x-axis opposite direction.

What does 'K' represent in the context of transformations?

Vertical translation along the y-axis. Signup and view all the answers

What does 'A' represent in an exponential function?

Orientation and shape; a 1 stretched vertically if 0 < |a| < 1. Signup and view all the answers

What are the characteristics of an exponential decay function?

Continuous, domain is all real numbers, range y > 0, asymptote is the x-axis. Signup and view all the answers

What is the exponential decay equation?

Y = a(1 - r)^t Signup and view all the answers

What is the exponential growth function equation?

Y = a(1 + r)^t Signup and view all the answers

To solve exponential equations, get a common ______, ignore base and solve.

base Signup and view all the answers

What is a logarithm?

Y = log_b x where b > 0 and b not equal to 1. Signup and view all the answers

The property of equality for logarithmic functions states that if log_b x = log_b y, then x = y.

True Signup and view all the answers

What is the product property of logarithms?

The logarithm of a product is the sum of the logs of each factor. Signup and view all the answers

What is the quotient property of logarithms?

The log of a quotient is the difference of the logs of the factors. Signup and view all the answers

What is the power property of logarithms?

Log of a power is the product of the log and its exponent. Signup and view all the answers

What are common logs?

Logs with base 10. Signup and view all the answers

What is the change of base formula?

log_a n = log n / log a Signup and view all the answers

What is the compound equation?

A = p(1 + r/n)^(nt) Signup and view all the answers

What is the transformation of the logarithmic function equation?

A log_b (x-h) + k Signup and view all the answers

Study Notes

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.

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Description

This set of flashcards covers key concepts from Chapter 7 of Algebra 2. Each card features important definitions and characteristics related to exponential functions and their transformations. Ideal for students looking to reinforce their understanding of this chapter's material.