4.3 Curve Sketching
Objectives:
1. Given a graph, determine the asymptotes.
2. Determine the asymptotes of a function.
3. Sketch the graph of the function given different information.
4. Sketch a graph of a function.
Given a graph, determine the asymptotes.
3 2( ) 2 3 12 2f x x x x= − + + +
y-intercept: x-intercept(s):
4 2( ) 2 3f x x x= − −
y-intercept: x-intercept(s):
3( )
2
xf x
x
+=
−
y-intercept: x-intercept(s):
Vertical Asymptote(s): Horizontal Asymptote:
2( )
16
xf x
x=
−
y-intercept: x-intercept(s):
Vertical Asymptote(s): Horizontal Asymptote:
2
2
1( )
25
xf x
x
−=
−
y-intercept: x-intercept(s):
Vertical Asymptote(s): Horizontal Asymptote:
