math III

• what are the number categories?

  N= {1, 2, 3...}

  W={0, 1, 2, 3...}

  Z={...-2, -1, 0, 1, 2...}

  Q= any number that can be written as a fraction

  I= any number that can't be written as a fraction

  R= real numbers
• what are the number properties?

  commutative property is when order doesn't matter

  associative property is when grouping doesn't matter

  distributive is when you distribute the number outside of the parantheses

  identity is when you add 0 to a number to get itself, or multiply a number by 1 to get itself

  inverse is when you add the inverse of a number to get 0, or multiply the reciprocal of a number to get 1
• what is ADESI?

  Annotate: focus where?

  Define: what varies? what does not? label variables

  Equation: what is the relationship?

  Solve: what technique?

  Interpret: reasonability, units, sentance
• absolute value is the magnitude of a number, the distance from the origin to the number on the number line
• a function is when each x value only corresponds to one y value
• how do you solve absolute value equations?


  isolate the bars

  rewrite the equation as a disjunction

  solve

  check for extraneous solutions
• domain: input, independent, x
• range: output, dependent, y
• standard linear form?


  Ax+By=C
• point-slope form?


  y-y1=m(x-x1)
• slope intercept form?


  y=mx+b
• f(x)=a(x-h)+k


  a= direction of opening, narrower/wider

  h= horizontal translation, opposite sign (x-intercept)

  k= vertical translation (y-intercept)
• complex number: a number that can be written in the form (a+bi) where i= radical -1 and a, b are real numbers
• complex conjugate: (a+bi)(a-bi)
• complex absolute value: distance from origin on the complex plane


  solve using a^2+b^2=c^2 (make a triangle on complex plane)