Composition of Functions

Chapter 6

1. Definition of Sine and Cosine. (p241)
Example: sec6.2: 5, 7.

2. Coordinates of a Point on a Circle of Radius r .(p243)
Example: sec6.2: 11, 12.

3. Definition of Radians. (p247)

4. Converting between Degrees and Radians



Example: sec6.3: 9-14

5. Arc Length (p249)
Example: sec6.3: 26, 27.

6. Sinusoidal Functions
For the sinusoidal functions

y = Asin(B(t − h)) + k
y = Acos(B(t − h)) + k

(a) | A |is the amplitude.

(b) h is the horizontal shift.

(c) 2π / | B | is the period.

(d) y = k is the midline.

Example: sec 6.5: 9, 10.

Chapter 8

1. Composition: The function f (g(t)) is said to be a composition of f with g . The function

f (g(t)) is defined by using the output of the function g as the input to f .

Composition of functions defined by formulas , graphs, tables

Example: sec8.1: 5, 21, 29.

2. Combinations of Functions

The difference of two functions The quotient of two functions

Example: sec8.3: 9, 19.

Chapter 9

1. Definition of Power Functions (p377).

Graphs of power functions y = x^p :

(a) Positive integer powers: p = 2,4,6,..., and p = 3,5,7,....

(b) Negative integer powers: p = −2,−4,−6,..., and p = −1,−3,−5,....

2. Definition of Polynomial Functions (p386).