1. Week 1 Sketching graphs of functions General tips: be neat,
always label the axis,
give as much detail as possible.
Features you need to pay attention to:
intercepts,
local extrema, inflection points,
behaviour as x → ∞, horizontal & oblique asymptotes,
vertical asymptotes.

2. y = 3x, y = 3x + 2, y = –3x ; y = ex, y = –ex, y = e–x, y = e2x ;
Example 1:
y = 3x, y = 3x + 2, y = –3x ;
y = ex, y = –ex, y = e–x, y = e2x ;
y = ln x, y = ln x2 ;
y = sin x, y = cos x .
Example 2:
y = x2 + x – 2, y = x2 – 2x + 2, y = 1 – x2 ;
y = x3, y = x3 – x, y = x3 + x2 – 2x.

3. y = | x | ; x2 + y2 = 9, y = – (9 – x2)1/2 ; Example 3: Example 4:

4. Example 6:
Given the graph of the function y = f(x):
sketch, in as much detail as possible, the graph of y = f '(x).

5. Example 7:
Given the graph of the function y = f '(x):
sketch, in as much detail as possible, the graph of y = f (x). Assume that f (0) = 1.