Aug24

January 29

section covered in text
1.2. New Functions from Old Functions

objective

to be able to identify basic functions
to understand the ideas of transformation of functions
to understand the ideas of composition of functions

key ideas and/or vocabulary
constant functions, power functions, root functions, polynomials (coefficients, degree), linear function, quadratic, cubic functions, rational functions, algebraic functions (try to graph the functions in Figure 9 on your calculator at home), trigonometric functions, exponential functions, logarithmic functions, transcendental functions, translations, stretching transformations, shrinking transformations, completing the square, composition of functions

study how polynomials "look", i.e. what happens to the value of the functions as x approaches infinity or -infinity, and how many roots are there

when do we have asymptotes?

exponential and logarithmic functions as inverses

solved problems - using key ideas

distinguishing between types of functions, #2
using transformations on an arbitrary function, #5
using transformations on a specific function, #17
a study of the reciprocal of a given function, #28
composition of functions, #35
composition of three functions, #38
taking a verbal description of a function and changing it to an algebraic description of a function, #47

group work
none

announcements
Homework. #4,6,8,20,30,36,48 (due 2/5)

QUESTION OF THE DAY

What is the domain of the following function? Graph the function in a window of size [0,5] x [-7,2].

SOLUTION

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SOLUTION. The radicand 4x - 4 > 0 which implies x > 1. The domain is (1,¥).

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