4.5 – Summary of Curve Sketching Math& 151 Warnock - Class Notes

Here are the Guidelines for Sketching a Curve.

A. Domain B. Intercepts C. Symmetry Even:

Odd:

Period:

D. Asymptotes

Horizontal:

Vertical:

E. Increasing/Decreasing

0 or 0f x f x

F. Local Max or Min Values

G. Concavity/Inflection Points

H. Sketch the Curve!

#1) Use the guidelines to sketch the curve 2

2

2

1

xyx

.

f x f x

f x f x

f x p f x

,

limx a

x x

f x

#2) Sketch the graph of 2

1

xf xx

.

#3) Sketch xf x xe .

#4) Sketch 2cos sin2f x x x .

#5) Sketch 2ln 4f x x

.

Some curves have asymptotes that are ______________, neither horizontal nor vertical.

That is, lim ( ) 0x

f x mx b

.

This line, y mx b , is called a ___________ _________________________

which we will use __________ _____________________ to find.

#6) Sketch the graph of 3

2 1xf x

x

.