#AP Precalculus: Unit 2 Study Guide - Exponential and Logarithmic Functions

Welcome to your ultimate guide for Unit 2! This unit is all about exponential and logarithmic functions, which are super important for modeling real-world stuff. Let's get this bread! 🍞

This unit is a big deal, so make sure you understand these concepts well. You'll see them pop up in both multiple-choice and free-response questions.

#🧭 Unit 2 Overview: Exponential and Logarithmic Functions

This unit focuses on understanding and applying exponential and logarithmic functions. These functions are essential for modeling growth, decay, and various other phenomena. You'll learn to graph, analyze, and manipulate these functions, and see how they connect to sequences, composite functions, and inverse functions.

• Exponential functions: Form $f(x) = ab^x$, where 'a' and 'b' are constants, and b > 0 and not equal to 1. They model situations with growth or decay proportional to the current value.

• Logarithmic functions: In the form $f(x) = \log_b(x)$, they are the inverse of exponential functions. They model situations where the rate of change is inversely proportional to the current value.

You'll also learn to:

• Graph and analyze these functions, including their asymptotes, domain, and range.
• Solve exponential and logarithmic equations.
• Use properties of logarithms to simplify expressions.
• Use semi-log plots to analyze exponential data.

#🔨 Unit Breakdown

#🔷 Arithmetic & Geometric Sequences

Sequences are foundational to understanding patterns and growth. Let's break them down:

• Arithmetic Sequences: Each term differs by a constant amount (common difference, 'd').
  • Formula: $u_n = a + (n-1)d$, where 'a' is the first term.
  • Example: 1, 3, 5, 7.....