graph

graph

1. transformations types: rigid and nonrigid

   • Rigid transformations do not change the basic shape of the graph: horizontal shifts, vertical shifts, and reflections
     • f(x)=a(x-h)^2+k, k is the vertical shift, h is the horizontal shift
     • Reflection: g(x) = - f(x) , g(x) is the reflection of f(x) in the x-axis, g(x)=f(-x) , g(x) is the reflection of f(x) in the y-axis
   • Nonrigid transformations distorts the shape of the original graph: vertical stretch and vertical shrink, horizontal stretch and horizontal shift.
     • vertical: g(x)=cf(x)
       • stretch: c>1
       • shrink:0<c<1
     • horizontal: h(x)=f(cx)
       • stretch: 0<c<1
       • shrink: c>1

2. can be presented by dot, bar, line

   • Mathematical equation: a mathematical equation that approximates the relationship between t and E; E=at+b
   • Scatter plot: the graph of sets of of ordered pairs that are written from collected data
     • positive correlation: if y tends to increase as x increases
     • negative correlation: if y tends to decrease as x increases
     • Fitting a line to data
       • finding the line that goes two points
       • finding the line using a table

3. parent graphs

   • quadratic: y=x^2
   • cubic: y=x^3
   • radical: y= (square root)x
     • y= (square root)(x)
       • y= (square root)(-x)
         • y= -(square root)(-x)
       • y=- (square root)(x)
     • y= (square root)(x^2-a^2), Q I,II pf hyperbola
       • y= -(square root)(x^2-a^2), Q III,IV pf hyperbola
     • y= (square root)(a^2-x^2)Q I,II of half circle
       • y= -(square root)(a^2-x^2)Q III,IV of half circle
   • linear: y=x
   • rational: 1/x