# Graphs of Functions

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## Lecture Notes

#### Graphing Functions: Translation

PDF#
Page 1 to page 2

Methods for changing a function to shift it left, right, up, or down. Includes three examples.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Graphing Functions: Changing Scale

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Page 2

Ways to stretch or shrink a function by changing the expression used to define it, with an example.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Graphing Functions: Even and Odd Functions

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Page 2 to page 3

How to reflect a function across either of the coordinate axes, including definitions for even and odd functions. Rules for the behavior of even and odd functions are given, along with examples.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Graphing Functions: Trigonometric Functions

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Page 3 to page 6

Graphs of the sine, cosine, and tangent functions, including definitions of periodicity and the general sinusoidal wave, with examples.

Instructor: Prof. David Jerison
Prior Knowledge: None

#### Graphing Functions: Inverses

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Page 6 to page 8

Reflecting a graph across the line y=x to create an inverse function. Includes examples and discussion of the need to restrict the domain of the inverse function in some cases.

Instructor: Prof. David Jerison
Prior Knowledge: None

## Practice Problems

#### Complete Graph Analysis(18.01, Fall 2005)

PDF
Problem 1 (page 1 to page 2)

Graphing a function and finding its asymptotes, maxima, minima, inflection points, and regions where the graph is concave up or concave down.

Instructor: Prof. Jason Starr
Prior Knowledge: None

## Exam Questions

PDF - 2.2 MB#
Problem 1A-1 (page 1) to problem 1A-9 (page 2)

Nine questions involving translation, change of scale, even functions, odd functions, inverses, and trigonometric functions.

Instructor: Prof. David Jerison
Prior Knowledge: Graphing Functions (CR-G)