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In this lecture we review some precalculus concepts from a point of view that will get us ready to study calculus.
Quick Question
Is this the graph of a function?
Answer
Outline
Outlines for Lines in the Plane Functions and their Graphs Defining New Functions from Old
Textbook
Lines in the Plane
Functions and their Graphs
Defining New Functions from Old
Today's Homework
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Quiz
Lines in the Plane Quiz
Functions and their Graphs Quiz
Defining New Functions from Old Quiz
Examples

L_{1} be the line ax + by = c, where a, b, and c are constants. What is the equation of the line perpendicular to L_{1}, passing through the point (0, c)?

Find the equation of a line through (1, 1) perpendicular to a line passing through (1, 2) and (3, 5).

Consider a triangle with vertices (1, 1), (9, 7), and (3, 11). Do the perpendicular bisectors of the sides of the triangle intersect in a single point?

Examine the graph of the equation x^{2} + y^{2} = 4 for symmetry.

Find the domain of a rational function

Discuss the symmetries of a function

Consider two functions, and find the domains of their compositions

Find the inverse of a cube root function, and the domains of the function and its inverse

Find inverses from a table
Applets
 Symmetry: Odd and Even Functions
 Function Grapher
 Stretching Graphs
 hifting Graphs
 New Functions from Old
 New Functions from Old Game
 Arithmetical Operations on Functions
 Inverse Functions
Videos
 Is f(x) even, odd, or neither?
 cos(x)
 1/(x^{3} + x^{5})
 x·e^{x^2}
 cos(2x) + 3
 sin(x) + x^{2}
 Find domain and range from a sketch
 Given domain and range of f(x), find domain and range of g(x) = f(1 – x)
 Given domain and range of f(x), find domain and range of g(x) = f(x^{3}) – 1
 Given domain and range of f(x), find domain and range of g(x) = 2f(2x) – 1
 find the domain and range of f(x) = –12 – 10√x
 find the domain of f(x) = 10 / (5 – √(100 – x))
 find the inverse function of f(x) = 12 + x^{(1/3)} / 2

Find the line parallel to y = 1/2 x – 1.

Find the line perpendicular to the line connecting (6, –2) and (4, –4) that passes through the midpoint of the segment joining these points.
