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Calculus Prerequisites and Functions Overview

Learn linear equations, functions, graphs, exponential functions, logarithms, & trigonometric functions. Understand key concepts for calculus.

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Calculus Prerequisites and Functions Overview

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  1. AP Calculus AB/BC Chapter 1 Review Prerequisites for Calculus

  2. Linear Equations • Point-Slope Equation: • Slope-Intercept Form: y = mx + b • Parallel Lines: Slopes are equal • Perpendicular lines: Slopes are Opposite Reciprocals

  3. Functions and Graphs • Even Function: f(-x) = f(x) • Odd Function: f(-x) = -f(x) • Domain: The set of x-values which can be used in a function. • Range: The set of y-values resulting from the output of a function. • f◦ g = (f ◦ g)(x) = f(g(x)) • Piecewise Functions

  4. Exponential Functions • y = k∙ a x, k > 0 • If a > 1, then y is an exponential growth function • If 0 < a < 1, then y is an exponential decay function • Half-life: a = ½

  5. Functions and Logarithms • f-1(x) denotes the inverse function • To find an inverse, solve for x, switch x & y, the new function is f-1(x) • Logs are inverses of Exponential Functions • y = bx if and only if x = logby

  6. Trigonometric Functions • Memorize trig definitions • Know domain of sin, cos, tan • Know range of transformations

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