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• Operations on functions
  '''Example (intercepts).''' For a function $F:{\bf R}\to {\bf R}$, its graph is the following set given presented via Suppose $y=F(x)$ is a numerical function. Then the $x$-''intercepts'' of $F$ are the elements of the intersection of
  142 KB (23,566 words) - 02:01, 23 February 2019
• Functions
  [[image:boys and balls -- relation and function.png| center]] [[image:boys and balls -- function.png| center]]
  151 KB (25,679 words) - 17:09, 20 February 2019
• Classes of functions
  Now, what if ''all'' boys prefer basketball? Then the “preference function” $F$ cannot be simpler: all of its values are equal and all arrows point The table of this function $F$ is also very simple: all crosses are in the same column; and the graph
  143 KB (24,052 words) - 13:11, 23 February 2019
• Limits and continuity
  One of the most crucial properties of a function is the integrity of its graph: ''is there a break or a cut?'' For example, If there is a jump in the graph of the function, it can't represent motion!
  107 KB (18,743 words) - 17:00, 10 February 2019
• Calculus I, the discrete version
  *a node function $f: 0\mapsto 2,\ 1\mapsto 4,\ 2\mapsto 3,\ ...$; and *an edge function $s: [0,1]\mapsto 3,\ [1,2]\mapsto .5,\ [2,3]\mapsto 1,\ ...$.
  64 KB (11,521 words) - 19:48, 22 June 2017
• Differentiation
  ...What this means is that this procedure is a special kind of function, a ''function of functions'': ...hat this means is that this process is a special kind of function too, a ''function of functions'':
  82 KB (14,116 words) - 19:50, 6 December 2018
• Precalculus
  ...the ''signs'' of these numbers, it can be restated in terms of the ''sign function'': Such an implicit relation between two variables is called a ''function''. This is the data:
  100 KB (16,148 words) - 20:04, 18 January 2017
• Calculus exercises: part I
  It's just a limit. But we recognize that this is the derivative of some function. We compare the expression to the formula in the definition: The function is computed in two steps. Indeed, if
  49 KB (8,436 words) - 17:14, 8 March 2018
• The derivative
  We approached the problem by plotting the location as a function of time: [[image:location as a function of time.png| center]]
  75 KB (13,000 words) - 15:12, 7 December 2018
• Differential calculus
  *maximize the function $A(W)=-W^2+50W$. [[image:cattle -- function 2.png| center]]
  84 KB (14,321 words) - 00:49, 7 December 2018
• Vector and complex variables
  ...real-valued functions of two variables. Consider $u=f(x,y)=2x-3y$, such a function: Consider another such function: $v=g(x,y)=x+5y$ is also a real-valued function of two variables:
  113 KB (18,750 words) - 02:33, 10 December 2018
• Series
  ...t is called its best linear approximation and its happens to be the linear function the graph of which is the tangent line at the point. The replacement is jus However, there is a more basic approximation: a constant function, $y=C(x)$.
  113 KB (19,100 words) - 23:07, 3 January 2019
• Integration
  Suppose a function $f$ is defined on an open interval $I$. Then a function $F$ defined on $I$ that satisfies $F' = f(x)$ for all $x$ is called an ''an ...eorem of Calculus).''' (I) Given a continuous function $f$ on $[a,b]$, the function defined by
  69 KB (11,727 words) - 03:34, 30 January 2019
• Precalculus exercises
  ...)=x^2+3x-10$. Find the $x$- and $y$-intercepts and sketch the graph of the function. ...$55$ and its leading term is $-1$. Describe the long term behavior of this function.
  17 KB (2,933 words) - 19:37, 30 July 2018
• Preview of calculus: part 3
  == Exponential Function == ==Exponent as a function==
  17 KB (2,498 words) - 15:06, 19 March 2011
• Calculus of chain maps
  First, $f$ has to be a function that takes nodes to nodes: ...h first and then attach edges to them. Therefore, we require from the edge function $f$ the following:
  41 KB (7,344 words) - 12:52, 25 July 2016
• Continuous functions
  First we, informally, discussed continuity of a function as a transformation that does not tear things apart and interpreted this id <!--200-->[[Image:continuous function.png|center]]
  42 KB (7,138 words) - 19:08, 28 November 2015
• Differential equations
  ...re, the ''difference'' of a function $y$ defined at the primary nodes is a function defined at the secondary nodes of the partition: We can also think of this sequence as a function defined at the nodes of the partition:
  64 KB (11,426 words) - 14:21, 24 November 2018
• Limits: transition from discrete to continuous
  A function defined on a ray in the set of integers, $\{p,p+1,...\}$, is called an (inf Algebraically, we see that for every measure of closeness $\varepsilon$, the function's values become eventually that close to the limit.
  51 KB (9,271 words) - 20:02, 8 September 2016
• Systems of ODEs
  Every solution $x=x(t)$ and $y=y(t)$, when substituted into the function We turn instead to the actual function. First, we plot it with a spreadsheet ($\alpha=3$, $\beta=2$, $\gamma=3$, $
  63 KB (10,958 words) - 14:27, 24 November 2018

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