chapter 1 functions, graphs, and limits. copyright © houghton mifflin company. all rights...
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Chapter 1
Functions, Graphs, and Limits
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Figure 1.1: The Cartesian Plane
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Figure 1.2: Coordinateson the Cartesian Plane
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Figure 1.5: Pythagorean Theorem
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Figure 1.6: The Distance Formula
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Figure 1.10: The Midpoint Formula
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Figure 1.15 and Figure 1.16: (Shortcomings of the Point-Plotting Technique)
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Figure 1.17: Intercepts of a Graph
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Finding Intercepts
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Figure 1.20: Standard Formof the Equation of a Circle
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General Form of theEquation of a Circle
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Figure 1.23: Points of Intersection
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Figure 1.25 (Supply Curve), Figure 1.26 (Demand Curve), and Figure 1.27 (Equilibrium Point)
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Figure 1.30: Graphs ofMathematical Models
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Figure 1.31: The Slope-InterceptForm of the Equation of a Line
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Figure 1.32
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Figure 1.36: The Slope of aLine Passing Through Two Points
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Point-Slope Form of theEquation of a Line
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Figure 1.40: Linear Extrapolationand Interpolation
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Equations of Lines
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Parallel and Perpendicular Lines
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Definition of Function, Figure 1.43
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Figure 1.47: Definition ofComposite Function
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Figure 1.48: Definition ofInverse Function
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Figure 1.51
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Definition of the Limit of a Function
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Properties of Limits
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Operations with Limits
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The Limit of a Polynomial Function
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The Replacement Theorem
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Existence of a Limit
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Figure 1.60, Figure 1.61:Definition of Continuity
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Continuity of Polynomialand Rational Functions
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Definition of Continuityon a Closed Interval
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Figure 1.66: GreatestInteger Function
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Order of Operations
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Solving Equations
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