导言:函数和图表

“Ever since Isaac Newton used math to describe gravity, applied mathematicians have been inventing new mathematics or using existing forms to describe natural phenomena.” —Gino Biondini, professor
::“自艾萨克·牛顿用数学描述引力以来,应用数学家一直在发明新的数学,或使用现有形式描述自然现象。”

Mathematicians create functions, or models ,  to describe observations and phenomena in the world. These tools can be used to predict the outcome of events, and that is the value of creating and using mathematical functions. Mathematician Gino Biondini made recent advances in the study of waves. His team’s goal was to improve the wave equations first created in the 1700s, which predicted the behavior of waves, but broke down when waves  became  irregular. Biondini’s team showed mathematically that many different kinds of disturbances evolve to produce wave forms belonging to a single class. Their discovery provides a simpler set of categories for waves of all types,  so that scientists can make better predictions.
::数学家创造了描述世界观测和现象的功能或模型。 这些工具可以用来预测事件的结果,也就是创造和使用数学功能的价值。 数学家Gino Biondini在海浪研究方面最近取得了进步。 他的团队的目标是改善1700年代首次创造的波方程,这些波方程预测了海浪的行为,但当海浪变得非正常时,波方会崩溃。 比翁迪尼的团队从数学上表明,许多不同种类的扰动会演变成属于某一类的波形式。 它们的发现为各种波提供了更简单的类别,以便科学家能够做出更好的预测。

Mathematicians develop models that offer a type of map into the world of mathematical research and application. These methods allow exploration of often unseen worlds that can be used to predict, change, and improve our relationship with the world in which we live. 
::数学家开发模型,提供进入数学研究和应用世界的地图类型。 这些方法可以探索常常看不见的世界,用来预测、改变和改善我们与我们所生活的世界的关系。

In this chapter, we review and explore the primary concepts used to analyze functions and their graphs. The topics we cover, which will establish a foundation for further study, include function domain, range, extrema, symmetry, intercepts, asymptotes, continuity, transformations, composition, and inverses.
::在本章中,我们审查并探索用于分析函数及其图表的主要概念。 我们所覆盖的主题将为进一步研究奠定基础,包括功能域、范围、外形、对称性、拦截、无症状、连续性、转换、组成和反向。