chapter 1 functions, graphs, and limits. copyright © houghton mifflin company. all rights...

Chapter 1

Functions, Graphs, and Limits

Copyright © Houghton Mifflin Company. All rights reserved. 1 | 2

Figure 1.1: The Cartesian Plane


Figure 1.2: Coordinateson the Cartesian Plane


Figure 1.5: Pythagorean Theorem


Figure 1.6: The Distance Formula


Figure 1.10: The Midpoint Formula


Figure 1.15 and Figure 1.16: (Shortcomings of the Point-Plotting Technique)


Figure 1.17: Intercepts of a Graph


Finding Intercepts


Figure 1.20: Standard Formof the Equation of a Circle


General Form of theEquation of a Circle


Figure 1.23: Points of Intersection


Figure 1.25 (Supply Curve), Figure 1.26 (Demand Curve), and Figure 1.27 (Equilibrium Point)


Figure 1.30: Graphs ofMathematical Models


Figure 1.31: The Slope-InterceptForm of the Equation of a Line


Figure 1.32


Figure 1.36: The Slope of aLine Passing Through Two Points


Point-Slope Form of theEquation of a Line


Figure 1.40: Linear Extrapolationand Interpolation


Equations of Lines


Parallel and Perpendicular Lines


Definition of Function, Figure 1.43


Figure 1.47: Definition ofComposite Function


Figure 1.48: Definition ofInverse Function


Figure 1.51


Definition of the Limit of a Function


Properties of Limits


Operations with Limits


The Limit of a Polynomial Function


The Replacement Theorem


Existence of a Limit


Figure 1.60, Figure 1.61:Definition of Continuity


Continuity of Polynomialand Rational Functions


Definition of Continuityon a Closed Interval


Figure 1.66: GreatestInteger Function


Order of Operations


Solving Equations

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