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)