Function Basics Math Wiki


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Function Basics

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Function Basics Math Wiki

  1. 1. Basic Functions By: Alec Kargodorian, Bastiaan Grob, Haig Hadjian
  2. 2. Important Information • Functions are mathematical ideas that take one or more variables and produce a variable. • In an abstract mathematical sense, a function is a mapping of some domain onto some range. • For each item in the domain, there is a corresponding item in the range of the function. • Thus the domain is all of the possible inputs to the function and the range is all of the possible outputs. • Each item in the domain corresponds to a specific item in the range. • However, an item in the range may correspond to multiple items in the domain.
  3. 3. List of Functions 1. squaring function f(x) = x2 2. cubing function f(x) = x3 3. absolute value function f(x) = |x| 4. square root function f(x) = sqrt(x) 5. cube root function f(x) = cubeRoot(x) 6. natural exponential function f(x) = ex 7. natural logarithmic function f(x) = ln(x)
  4. 4. Definition • a function consists of an ordered triple of sets, written as (X,Y,F). • X is the domain of the function • Y is the codomain • F is a set of ordered pairs • A function basically gets an input and returns with an output like a machine • The graph of a function is its set of ordered pairs. • A relation is the set of ordered pairs • A domain is the set of first coordinates of the ordered pairs (x values) • A range is the set of second coordinates of the ordered pairs (y values)
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  6. 6. History The history of the function concept in mathematics is described by da Ponte (1992). The underlying idea of a function dates back to the Persian mathematician, Sharaf al-Dīn al-Tūsī, in the 12th century. In his analysis of the equation x3 + d = bx2 for example, he begins by changing the equation's form to x2(b − x) = d. He then states that the question of whether the equation has a solution depends on whether or not the “function” on the left side reaches the value d. To determine this, he finds a maximum value for the function. Sharaf al-Din then states that if this value is less than d, there are no positive solutions; if it is equal to d, then there is one solution; and if it is greater than d, then there are two solutions.