This week, we will cover the remainder of Chapter 2. Specifically, we will
- Chapter 2-3, 2-4: Quadratic
For quadratic functions we review vertex and intercepts.
- Chapter 2-4: Polynomial and Rational Functions
For general polynomial and rational functions we don't go into much
detail. A rational
function is a quotient of two polynomials.
For polynomials, we just look at the possible
shapes of the graph, specifically the number of intercepts and turning points
it can have. For rational functions, we look at the domain and at vertical
and horizontal asymptotes.
- Chapter 2-5 :
You have already seen the properties of exponential functions twice recently
in appendix A (once for integer exponents, once for rational exponents),
so those should be familiar. Now we look more at the properties of the graph of
Concentrate on learning the properties of bx with b>1.
The graph of an exponential curve with b<1 is just the reflection
in the y-axis of the exponential curve with 1/b>1. For example,
the same as 4-x.
All exponential graphs with b>1 look pretty much the same. The
one with b=e is just a special case. e is an important number
in mathematics that comes up in a lot of places where you wouldn't expect
it; sort of like π.
The application to compound interest will come back in chapter 3 (which we
won't cover until week 8). You can look ahead to chapter 3 for more explanations
on compound interest, if you want.
- Chapter 2-6:
This section is very important for solving equations involving exponentials.
This material may not be as familiar to you as the previous topics, or maybe
Read the textbook and do HW 3 in MyMathLab.
Note that a hard deadline for homeworks kicks in this week. We let students
add the course until the end of week 2, so we don't enforce homework deadlines
until week 3. The homework for this week, as well as earlier weeks, is due
by the end of week 3.
Wednesday, August 5, 2015