Graphing Functions: Translation
Methods for changing a function to shift it left, right, up, or down. Includes three examples.
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
Graphing Functions: Changing Scale
Ways to stretch or shrink a function by changing the expression used to define it, with an example.
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
Graphing Functions: Even and Odd Functions
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.
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
Graphing Functions: Trigonometric Functions
Graphs of the sine, cosine, and tangent functions, including definitions of periodicity and the general sinusoidal wave, with examples.
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
Graphing Functions: Inverses
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.
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
Complete Graph Analysis
Graphing a function and finding its asymptotes, maxima, minima, inflection points, and regions where the graph is concave up or concave down.
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18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr
Course Material Related to This Topic:
- Complete practice problem 1 on pages 1–2
- Check solution to practice problem 1 on pages 8–9
Graphing
Nine questions involving translation, change of scale, even functions, odd functions, inverses, and trigonometric functions.
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18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison
Course Material Related to This Topic:
- Complete
exam problems 1A–1 on page 1 to problems 1A–9 on page 2
- Check solution to
exam problems on pages 1–2
Sketching Graphs
Three problems which involve sketching the graph of a function.
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18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr
Course Material Related to This Topic:
- Complete exam problems 2.1 to 2.3 on page 2
- Check solution to exam problems 2.1 to 2.3 on page 2