Functions and Continuity
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The reciprocal function - singularities
The reciprocal function takes the form [Equation goes here - download the original pdf to see it.] The graph of the reciprocal function is the rectangular hyperbola. [Diagram goes here - download the original pdf to see it.] The graph illustrates important points about this function. At x = 0 the function is undefined because we cannot divide by zero. The expression[Equation goes here - download the original pdf to see it.] is meaningless. The graph shows this because around the origin the function tends to [Equation goes here - download the original pdf to see it.] as we approach x = 0 from the negative side, and tends to [symbol] as we approach x = 0 from the positive side. We say that there is a singularity of the function f at x = 0, which means that f is undefined there. The y-axis (x = 0) is an asymptote of f, but as f crosses the origin, x = 0, the value of [equation] jumps from [Equation goes here - download the original pdf to see it.] to [Equation goes here - download the original pdf to see it.].
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Contents of
Functions and Continuity
1 Functions
2 Graph
3 Inverse of a Function: monotone increasing or decreasing functions
4 The reciprocal function - singularities
5 Functions defined piecewise on their domain
6 Limits
7 Formal definition of a limit
8 Formal definition of the limit of a function at a point x = a
9 Informal arguments
10 Continuity
11 Combining limits
12 Quotients
13 Image set
14 Inverse image
15 Odd and even functions
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