Algebra 2 Chapter 6 Flashcards

Questions and Answers

What is the term for the formula used to calculate compound interest?

Compound Interest Formula (correct)

Continuous Compound Interest Formula

Power Property

Horizontal Translation

Which formula is used for continuous compounding of interest?

Product Property

Horizontal Shrink

Quotient Property

Continuous Compound Interest Formula (correct)

What is the product property in algebra?

The product property states that the multiplication of two powers with the same base can be simplified by adding their exponents.

What does the quotient property state?

The quotient property states that the division of two powers with the same base can be simplified by subtracting the exponents. Signup and view all the answers

What is the power property in algebra?

The power property states that when raising a power to another power, you multiply the exponents. Signup and view all the answers

What is a horizontal translation?

A horizontal translation is a shift of the graph of a function to the left or right along the x-axis. Signup and view all the answers

In the equation g(x) = 4^x ________________ + 5, what kind of translation occurs?

vertical translation Signup and view all the answers

What function represents reflection over the y-axis?

g(x) = 4^-x Signup and view all the answers

What is the function for reflection over the x-axis?

g(x) = -4^x Signup and view all the answers

What does a horizontal stretch imply in graph transformations?

A horizontal stretch occurs when the function g(x) = 4^(2x) reduces the rate at which the x-values increase. Signup and view all the answers

What is the function that represents a horizontal shrink?

g(x) = 4^(x/2) Signup and view all the answers

What does a vertical stretch entail?

A vertical stretch occurs when the function g(x) = 3(4^x) increases the rate at which y-values grow. Signup and view all the answers

What is the definition of vertical shrink?

A vertical shrink occurs when the function g(x) = 1/4(4^x) decreases the rate at which y-values increase. Signup and view all the answers

Study Notes

Compound Interest Formulas

Compound interest formula calculates the amount of interest on an investment or loan over time, typically compounded at specific intervals.
Continuous compound interest formula represents the limit of compounded interest as the compounding frequency approaches infinity, calculated with the formula A = Pe^(rt), where A is the amount, P is the principal, r is the rate, and t is time.

Properties of Exponents

Product property states that when multiplying two powers with the same base, you add the exponents: a^m * a^n = a^(m+n).
Quotient property explains that when dividing two powers with the same base, you subtract the exponents: a^m / a^n = a^(m-n).
Power property indicates that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(mn).

Graph Transformations

Horizontal translation occurs when the function is shifted left or right; exemplified by g(x) = 4^(x + 2), moving the graph 2 units to the left.
Vertical translation shifts the function up or down; indicated by g(x) = 4^x + 5, moving the graph 5 units upwards.
Reflection over the y-axis indicates a horizontal flip of the graph, demonstrated with g(x) = 4^(-x).
Reflection over the x-axis shows a vertical flip of the graph, represented by g(x) = -4^x.

Stretches and Shrinks

Horizontal stretch occurs when the x-values of the function are expanded, seen in g(x) = 4^(2x), which stretches the graph away from the y-axis.
Horizontal shrink makes the graph more narrow, illustrated by g(x) = 4^(x/2).
Vertical stretch amplifies y-values, exemplified by g(x) = 3(4^x), leading to a steeper graph.
Vertical shrink reduces the height of the graph, shown by g(x) = (1/4)(4^x), resulting in a flatter appearance.

Description

Test your knowledge of key formulas and transformation rules in Algebra 2, Chapter 6. This quiz covers essential concepts such as compound interest, properties of exponents, and translations of graphs. Perfect for reinforcing your understanding of these critical topics.