In this video we are going to take a look how to use a lot of information about function to draw a rough sketch of that function. In our examples we are going to collect a following information about function: domain and the range of a function, x and y intercepts, symmetry properties (is it: odd, even, neither odd nor even, periodic), asymptotes (vertical, horizontal, slant), critical points (f=0 or f undefined), increasing/decreasing intervals (f>0, f<0), inflection points (f=0 and f changes sign), concave up/down intervals (f>0, f<0), local maxima and minima (1st Derivative Test, 2nd Derivative Test). We are going to see how all these properties interact to create a shape of a graph.
these problems take a significant amount of time and care!
Start by looking
at the domain, range, intercepts, and asymptotes. Mark these on
Find the critical
points and mark these on your graph.
Finally, look at
slope and concavity information. Use this information to sketch the
graph by filling things in between the points you already have
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.