Functions

Functions

1. Characteristics

   • Domain x = (-infinite, -1) U (-1, infinite)
   • Codomain y = (-infinite, infinite)
   • Increases in (-infinite, -2) U (0, 2) U (2, infinite)
   • Decreases in (-2, -1) U (-1, 0)
   • Points of discontinuity x= -1 and x = 2
   • Relative maximum (-2,3) --- Relative minimum (0, 0)
   • Tends to increase until infinite
   • Verical asymptote in x = -1
   • ARC [-3, -2]
     • (3 - 2) / (-2 -3)
       • 1/5 > 0
         • Increases
   • Periodicity
     • Period = 6

2. Basic functions

   • Lineal
     • y = mx + n
     • Value chart
       • 2 values
   • Quadratic
     • y = ax*2 + bx + c
     • Points of cut with x edge and y edge
     • Value chart
       • Values near the vertex
     • Vertex
       • X = -b / 2a
       • Y = substitute X in the ecuation
   • Hyperbola
     • k / (x+a) + b
     • Domain
     • Vertical asymptote = point you remove from the R in the domain
     • Horizontal asymptote = b
     • Value chart
       • 2 before the V.A and 2 after it
   • Radical
     • Domain
     • Value chart (values inside de dom)
   • Exponential/ logarithmic
     • y = a*x / y = log*a x
       • Value chart
         • Exponential
           • x = -2, -1, 0 , 1 and 2
         • Logarithmic
           • The other way round the exponential (x in y, and y in x)

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