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Contents
Techniques
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Curve
Sketching Techniques
Important
Points
1.
X-intercepts. These can be found by putting y=0 and solve for x.
2.
Y-intercepts. These can be found by putting x=0 and solve for y.
3.
Stationary points. Found by calculating the derivative of the
function, set it to zero and solve for x.
4.
Asymptotes. Lines on the plane that the curve tends towards but does
not cut. Can be vertical, horizontal or oblique. Found by letting x or y
tend to infinity and check if the function approaches a certain value.
5.
Gradient. Is the gradient positive or negative for the relevant
portions of the graphs. It can be deduced from the derivative.
These
techniques can be used for any graph, especially if you do not know the
general shape of the graph.
 Example:
Sketch the graph of x2 - 2x - 3.
Solution:1.
Find y-intercept.
When x = 0, y = -3
2.
Find x-intercepts.
When y = 0, x2 - 2x - 3 = 0 --> x = 3 or x = -1
3.
Find stationary points.
dy/dx = 2x - 2 = 0
x = 1, y = 4
4.
Asymptotes: none
5.
Gradient.
When x is slightly less than 1, dy/dx < 0
When x is slightly greater than 1, dy/dx > 0
Mark
these points on a set of axes and draw a smooth curve through tem.
 More
examples in individual sections.
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