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2011-02-19 17:43:32
UK MA123 Calculus Gootman

Book by Elliot C. Gootman, Ph.D.
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  1. equation
    • a statement that two mathematical expressions are equal
    • describes a relationship between two quantities
  2. solution
    a set of numbers that can be substituted for the variables in an equation so that the equality is true
  3. A solution is said to _______ an equation.
  4. function
    a formula, rule or procedure for taking a set of numbers and assigning to each number x in the set precisely one value
  5. independant variable
    • x in f(x); can be picked to be more or less any number
    • an arbitrary number in the domain of a function f
    • plays the role of a "placeholder"
  6. f(x)
    f is a function of x
  7. dependant variable
    y = f(x) ; these values depend on those of x
  8. y = f(x)
    defining y as a function of x
  9. undefined
    when an equation or function makes no sense at a particular point, it is said to be undefined at that point
  10. domain
    the set of points where a function is defined
  11. codomain
    y; or the value of f at x
  12. range
    the set of all possible values of f(x) as x varies throughout the domain
  13. linear function
    • f(x) = mx + b
    • m = slope
    • b = y intercept
  14. quadratic function
    • f(x) = ax2 + bx + c
    • standard form = f(x) = a (x - h)2 + k
    • vertex = (h,k)
    • a > 0 parabola opens upward; a < 0 opens downward