AP Precalculus UNIT 2 Review: Exponential and Logarithmic Functions (Reteaching and Test Practice)

Unit 2: Exponential and Logarithmic Functions

2.1 Change in Arithmetic and Geometric Sequences
2.2 Change in Linear and Exponential Functions
2.3 Exponential Functions
2.4 Exponential Function Manipulation
2.5 Exponential Function Context and Data Modeling
2.6 Competing Function Model Validation
2.7 Composition of Functions
2.8 Inverse Functions
2.9 Logarithmic Expressions
2.10 Inverses of Exponential Functions
2.11 Logarithmic Functions
2.12 Logarithmic Function Manipulation
2.13 Exponential and Logarithmic Equations and Inequalities
2.14 Logarithmic Function Context and Data Modeling
2.15 Semi-log Plots

1. Arithmetic and Geometric Sequences:
- Arithmetic sequences: A sequence of numbers with a common difference between consecutive terms.
- Geometric sequences: A sequence of numbers with a common ratio between consecutive terms.

2. Graphing and Describing Exponential Functions:
- Exponential functions: Functions in the form f(x) = a^x, where "a" is a positive constant.
- These functions grow or decay rapidly as x changes, and they have a characteristic J-shaped graph.

3. Exponential Growth and Decay:
- Exponential growth: When a quantity increases exponentially over time.
- Exponential decay: When a quantity decreases exponentially over time.

4. Transformations and Manipulations of Exponential Functions:
- Transformations involve changing the parameters (a, b) and adding constants to shift and stretch the graphs of exponential functions.
- Manipulations include addition, subtraction, multiplication, and division of exponential expressions.

5. Composite Functions:
- Composite functions are formed by combining two or more functions by substituting one function's output as the input to another function.

6. Inverse Functions:
- Inverse functions "undo" the actions of another function, swapping the roles of input and output. If f(x) and g(x) are inverses, then f(g(x)) = x and g(f(x)) = x.

7. Logarithmic Functions:
- Logarithmic functions are the inverse of exponential functions, expressed as y = log_a(x), where "a" is the base of the logarithm.
- They measure the exponent to which a base must be raised to obtain a given value.

8. Natural Log:
- The natural logarithm, denoted as ln(x), has a base of "e" (approximately 2.71828).

9. Semi-Log Plots:
- Semi-logarithmic plots are graphs where one axis is in a logarithmic scale, and the other is in a linear scale. They are often used to visualize exponential growth or decay.

10. Word Problems Involving Logarithms and Exponents:
- These problems involve real-life situations where logarithms and exponents are used to model and solve various scenarios, such as population growth, compound interest, radioactive decay, and more.

These topics are fundamental in precalculus and serve as a foundation for more advanced mathematical concepts.

These concepts are fundamental in precalculus and serve as building blocks for more advanced mathematical topics.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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[lauren]

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