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.

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