Notes:
2/24    2/29

2/24

I. Homework from students:
pg 145, # 1- 4, 31, 39
pg 147 #35, 39, 49, 57, 61, 64
II. In notes, sketch, state domain and range.
1. f(x) = sqrt(x - 6) + 2
2. f(x) = 3x + 4
3. y = 1/(x + 5) - 2
Note: asymptote ARE DRAWN on a sketch when needed.
III. inverse
f -1(f(x)) = f(f -1(x)) = x
The inverse of the function equals the function of the inverse.
The inverse and the function undo each other resulting
in the original number.
IV. Calculator Problem: The vertical asymptote is
graphed as a part of a function even though it should not be.
Solution: In MODE or FORMAT select DOTS rather than CONNECTED.

2/29

I. Solve for y.
1.) x = y/4
2.) x = y + 6
3.)

II. Comment on odd and even functions:
Check out the mouth.
III. Inverse Functions
Before reviewing the material below, look at the notes and answers from last class.
If you click on the graph, the inverse is displayed.
IV. Determine the inverse of each function if one exists.
1. f(x) = sqrt(x - 6) + 2
2. f(x) = 3x + 4
3. y = 1/(x + 5) - 2

2/29/00: I.
1.) y = 4x
2.) y = x - 6
3.)
2/29/00: II.
1. f(x) = sqrt(x - 6) + 2
y = sqrt(x - 6) + 2
x = sqrt(y - 6) + 2
x - 2 = sqrt(y - 6)
(x - 2)2 = (sqrt(y - 6))2
(x - 2)2 = y - 6
(x - 2)2 + 6 = y
f -1(x) = (x - 2)2 + 6

2. f(x) = 3x + 4
y = 3x + 4
x = 3y + 4
x - 4 = 3y
(x - 4)/3 = 3y/3
(x - 4)/3 = y
f -1(x) = (x - 4)/3

3. y = 1/(x + 5) - 2
x = 1/(y + 5) - 2
x + 2 = 1/(y + 5)
(x + 2)/1 = 1/(y + 5)
1/(x + 2) = (y + 5)
1/(x + 2) = y + 5
1/(x + 2) - 5 = y
f -1(x) = 1/(x + 2) - 5

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