Curve Sketching - Rational Function (Exam Question Example)

Taken from 2017 WACE Specialist Mathematics Exam

Question 5 (6 marks)

I hope my explanation helps :)

For the function y=f(x)/g(x)
x-intercepts: f(x)=0
y-intercept: f(0)=a
Vertical asymptotes: g(x)=0
Horizontal asymptotes lim[f(x)/g(x)] as x approaches plus/minus infinity

This calculus video tutorial provides a summary of the techniques of curve sketching. It shows you how to graph polynomials, rational functions with horizontal & vertical asymptotes and square roots using the first derivative and the second derivative of the functions. This video contains plenty of examples and practice problems for you to work on.

Here is a list of topics.
1. Summary of Curve Sketching
2. Increasing and Decreasing Functions - First Derivative
3. Local & Relative Maximum and Minimums - First Derivative Test
4. Critical Points & Inflection Points
5. Concavity - Concave up and Concave Down Curves - Second Derivative is Positive & Negative
6. Graphing Polynomial Functions
7. Sketching Rational Functions With Horizontal and Vertical Asymptotes
8. Curve Sketching with Square Root Functions
9. Techniques of Differentiation - Power Rule, Product Rule, Quotient Rule, and Chain Rule