Algebra is generous, she often gives more than is asked of her.

D'Alembert

sections:

      1.2, 1.3, 1.4, 1.5, 1.6, 1.7, and 1.8

Much of this chapter considers the concept of a function; the graphs of functions, and operations combining functions.

objectives:

• 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
• 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
• scale the graph of a function
• 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
• use symmetry to help sketch the function
• 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 from the graph of a function