Podcast
Questions and Answers
What is the term for the formula used to calculate compound interest?
What is the term for the formula used to calculate compound interest?
Which formula is used for continuous compounding of interest?
Which formula is used for continuous compounding of interest?
What is the product property in algebra?
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?
What does the quotient property state?
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What is the power property in algebra?
What is the power property in algebra?
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What is a horizontal translation?
What is a horizontal translation?
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In the equation g(x) = 4^x ________________ + 5, what kind of translation occurs?
In the equation g(x) = 4^x ________________ + 5, what kind of translation occurs?
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What function represents reflection over the y-axis?
What function represents reflection over the y-axis?
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What is the function for reflection over the x-axis?
What is the function for reflection over the x-axis?
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What does a horizontal stretch imply in graph transformations?
What does a horizontal stretch imply in graph transformations?
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What is the function that represents a horizontal shrink?
What is the function that represents a horizontal shrink?
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What does a vertical stretch entail?
What does a vertical stretch entail?
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What is the definition of vertical shrink?
What is the definition of vertical shrink?
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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.
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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.
