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Unit One: AP Calculus AB, The exponential graph is blue and the…
Unit One: AP Calculus AB
Trigonometric Functions
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A trigonometric function is a function that either uses sine, cosine, or tangent. both sine and cosine are represented on a graph as waves where tangent is represented as repeated shapes that look almost like the letter S that are separated by asymptotes. Tangent is blue, cosine is red, and sine is black in the example below.
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Logarithmic Functions
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Logarithmic functions are used to represent a relationship where one of the variables grows constantly and the other variable grows to the power of the first variable. Logarithmic functions are commonly used to help figure out exponential decay and growth if the period, total time present, or both are not present in the given information.
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Parametric Functions
When using parametric functions with trigonometric functions, you can easily create circles and ellipses
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A parametric function is a function that uses parameters to help represent different shapes and images when visualized on a graph. They can come in many shapes and sizes and when using them in combination with piecewise functions, you can create almost any shape imaginable.
Exponential Functions
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When used together (example sin(x^2)) the frequency of each ripple in the sin graph becomes exponentially quicker.
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Exponential functions are used to represent a relationship where one of the variables grows constantly and one grows to the power of said variable
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Functions and Graphs
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Graphs are used to visually represent all types of functions. This includes trigonometric functions by using sin and cosine waves and tangent with s shaped curves. It represents parametric functions by identifying each part of the parametrized function. It represents logarithmic and exponential functions with the same curve although they are each oriented differently.
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Lines
All functions are essentially derived from a basic line. A basic line is manipulated to create different shapes and represent different functions
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Lines are the cornerstone of functions and are represented by the iconic y=mx+b equation. It is used to represent linear relationships between different variables and allows students to be introduced to functions for the first time without overwhelming them.
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