Calculus on Demand at Dartmouth College Lecture 1 | Index | Lecture 3 Lecture 2

## Resources

Math 3 Course Syllabus
Practice Exams

# 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?

### 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

### 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