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Graphs and Functions
Barnett, Ziegler, and Byleen, chapter 3
A picture equals a thousand words.
A function equals a "pair of graph."
sections:
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
This chapter introduces the Cartesian coordinate system and the concept of a function. The Cartesian
coordinate system is useful to represent pictorially the behavior of functions. We also wish to combine
functions, one particular combination called composition leads to the concept of an inverse function.
objectives:
- graph pairs of points on a Cartesian coordinate system
- explain what the abscissa and ordinate are
- tell what is meant by the graph of a relationship
- determine the symmetry of a graph with respect to the x-axis, the y-axis, and the origin
- generate a graph by plotting points
- determine the distance between two points
- recognize the equation of a circle
- from the equation of a circle determine the center and the radius
- recognize the equation of a straight line
- graph a straight line
- tell what is meant by the slope of a straight line
- determine the x and y intercepts
- compute the slope from two points
- determine the equation of a line from a slope and a point
- write out the equations for vertical and horizontal lines
- define the term function
- use the functional notation
- distinguish between dependent and independent variable
- classify a relation or mapping as a function or non-function
- explain what is meant by domain and range
- determine the domain of a function
- determine the range of a function
- compute the natural domain of a function
- graph a function in a Cartesian coordinate system
- describe the graph of a linear function
- distinguish between a linear function and a constant function
- describe the graph of a quadratic function
- determine the axis-of-symmetry for a quadratic function
- compute the coordinates of the vertex of a quadratic function
- determine the domain and range of a function from a graph
- use the vertical line test
- shift the graph of a function vertically
- shift the graph of a function horizontally
- ascertain the intervals that a function is increasing or decreasing
- define what is meant by an odd or even function
- tell whether a function is odd, even, or neither
- relate the oddness or evenness of a function to symmetry about the axes and the origin
- plot piecewise defined graphs
- express the sum, difference, product, and quotient of two functions
- determine the domain and range of combined functions
- calculate a composite function
- determine the domain and range of the composite
- explain what is meant by one-to-one
- ascertain whether a function is one-to-one
- compute a appropriate restricted range over which a function might be one-to-one
- use the horizontal test
- explain what an inverse function is
- calculate the inverse of a function
- determine the graph of an inverse function the graph of a function
- write out appropriate functions from application situations
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© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner |