A Summary of Curve Sketching Lesson 4.6

How It Was Done BC (Before Calculators) How can knowledge of a function and it's derivative help graph the function? How much can you tell about the graph of a function without using your calculator's graphing? Regis might be calling for this information!

Algorithm for Curve Sketching Determine domain, range of the function Determine critical points  Places where f ‘(x) = 0 Plot these points on f(x) Use second derivative f’’(x) = 0  Determine concavity, inflection points Use x = 0 (y intercept) Find f(x) = 0 (x intercepts) Sketch

Recall … Rational Functions Leading terms dominate  m = n => limit = a n /b m  m > n => limit = 0  m asymptote linear diagonal or higher power polynomial

Finding Other Asymptotes Use PropFrac to get If power of numerator is larger by two  result of PropFrac is quadratic  asymptote is a parabola

Example Consider Propfrac gives

Example Note the parabolic asymptote

Other Kinds of Functions Logistic functions Radical functions Trig functions

Assignment Lesson 4.6 Page 255 Exercises 1 – 61 EOO