Graphing Techniques
Lesson 2: More Features
The usual features of a graph's sketch includes:

Asymptotes

Axial intercepts

Stationary points
(2) Axial intercepts
Axial intercepts refer to the points where the graph cuts the x and the y axes.
(A) y intercept
It is obtained when x = 0.
(B) x intercept
It is obtained when y = 0.
Example 1
Find the axial intercepts of the following equations:
(a)
(b)
(c)
Solution
(a)
(b)
(c)
(3) Stationary points
Stationary points are located when the gradient of the graph = 0.
Example 2
Find the exact stationary point(s) of the graph given by
Solution
NOTE:
All the features (except for asymptotes) can be obtained from the graphic calculator. However the graphic calculator may not provide exact values.