Graphs Axis, Stationary Points and Asymtotes

GCE O-level and GCE A-Level Mathematics. IGCSE. IB Diploma HL SL Mathematics.
Some common features of a graph.
Axial Intercepts
  • also known as y-intercepts and x-intercepts (roots of an equation)
  • this occurs at x=0 for y-intercepts, and y=0 for x intercepts
  • substitute the above into equation of curve for the intercepts
Stationary points
  • gradient, m, dy/dx=0
  • tangent lines at stationary points are parallel to the x-axis (horizontal)
  • stationary points can be minimum/maximum/inflexion
Asymptotes
  • an asymptote is a line that values of x or y tend towards when reaching infinity ∞
  • there are 3 types of asymtotes: horizontal, vertical and oblique
  • when y tends to infinity and x tends to a number, a vertical asymptote occurs
  • when x tends to infinity and y tends to a number a horizontal asymptote occurs
  • an oblique asymptote occurs when f(x)/g(x) where f(x) is one degree higher than g(x)

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