A Summary of Curve Sketching

What should you consider?

• symmetries• x-intercept• y-intercept• relative extrema• asymptores• concavity• inflection points• intervals of increase• interval of decrease

ASYMPTOTE – VA HA SA

VERTICAL ASYMPTOTE

HORIZONTAL ASYMPTOTE

SLANT ASYMPTOTE

Long divide N(x) by D(x)

Let’s see how that works!!!

Sketch the graph of the equationexample

VA: HA: m = n

-4 4

- + -

Almost Done !!!!

-4 4/3 4

- - + -

Let’ make a list

• x-intercept• y-intercept• VA• HA• SA• f(x) • f(x) • X max• X min

• f(x)

• f(x)

• X infl

Sketch the graph of the equationexample

• x-intercept• y-intercept• VA• HA• SA• f(x) • f(x) • X max• X min

• f(x)

• f(x)

• X infl

• x-intercept• y-intercept• VA• HA• SA• f(x) • f(x) • X max• X min

• f(x)

• f(x)

• X infl

Sketch the graph of the equationexample