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Contents In this lecture we review some pre-calculus 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 Log into WebWorK Quiz Lines in the Plane Quiz Functions and their Graphs Quiz Defining New Functions from Old Quiz Examples L1 be the line ax + by = c, where a, b, and c are constants. What is the equation of the line perpendicular to L1, 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 x2 + y2 = 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/(x3 + x5) x·ex^2 cos(2x) + 3 sin(x) + x2 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(x3) – 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.

Lecture 1 | Index | Lecture 3