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: