1: Relating Changing Quantities
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- 1.1: Changing in Tandem
- Mathematics is the art of making sense of patterns. One way that patterns arise is when two quantities are changing in tandem. In this setting, we may make sense of the situation by expressing the relationship between the changing quantities through words, through images, through data, or through a formula.
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- 1.5: Quadratic Functions
- After linear functions, quadratic functions are arguably the next simplest functions in mathematics. A quadratic function is one that may be written in the form q(x)=ax²+bx+c, where a, b, and c are real numbers with a≠0. One of the reasons that quadratic functions are especially important is that they model the height of an object falling under the force of gravity.
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- 1.6: Composite Functions
- Recall that a function, by definition, is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value. Because every function is a process, it makes sense to think that it may be possible to take two function processes and do one of the processes first, and then apply the second process to the result.
Thumbnail: The average rate of change of an abstract function \(f\) on the interval [a,b].