© Azzolino


Notes:
2/17/00    2/22/00


2/17

I. For homework:
page 114 # 82
page 127 # 75
II. Problems from the book:
pg 125 # 25, 29, 45, 46, 56, 59, 60, 61, 62
III. Vocabulary:
The greatest integer function is a nickname for the greatest integer less than or equal to the specific number function.
IV. Calculator Techniques
a.)     Many calculators list the greatest integer function in MATH, NUM (for number), int().
b.)     If you wish the calculator to display
not
go to MODE and select DOT not CONNECT.
 
c.)     To read from a calculator screen to 2 decimal place accuracy the maximum value of a function (some y value) use the following calculator features.
1st: Store the function in the y= menu.
 
2nd: Press the GRAPH key to display the graph of the function.
 
3rd: Press TRACE and move to the right or left on this function to display a decimal approximation of the x value and the y value, the value of the function.
   
4th: If the decimal approximation of the y value changes in the first two decimal digits, it is necessary to redraw the function with a different viewing window.
 
5th: Press ZOOM then 1 for BOX to return to the graph to select the corner of a new window.
 
6th: Move the curser to a point which will serve as one corner of a new viewing window.
I like keeping the viewing window the same shape as the viewing window of the calculator. I pick a corner which builds this shape rectangle about the region of the graph which needs enlargeing.
 
7th: Press ENTER to make the corner "stick" and watch how the curser changes shape on the screen.
 
8th: Move the curser to the diagonally opposite corner and watch as the new rectangular screen is created by your use of the curser.
 
9th: Press ENTER to make the corner "stick" on the new corner and watch as the graph is redrawn with better resolution.
 
10th: Repeat steps 3 through 9 until curser movement does not produce a change in the first two decimal digits of the y value.
 
d.) To keep a function in storage but not display the graph,
1st: Go to the y= menu
2nd: Move to the equal sign on the line with the desired function.
3rd: Press ENTER (on a TI82 or TI83) so that the equal sign is no longer highlighted.
3rd: Press Deselect (on a TI85 or TI86) on the soft key pad.

2/22

I. In your notes, sketch each and place work in two columns as shown.
1. y = x 2. y = x²
3. y = x3 4. y = x4
5. y = x5 6. y = x6
7. y = 1/x 8. y = 1/x²
II. Sketch, state domain, range.
9.) (x-2)2
9a.) -x2 + 3
10.) |x|
III. Vocabulary
polynomial   asymptote
odd function     f(-x) = -f(x)
Ex. f(x)=sin(x)
Ex. y = 1/x












even function   f(-x) = f(x)
Ex. f(x)=cos(x)
Ex. y = 1/x²












IV. Decomposition (taking apart) of functions -- Sketch then determine the functions which produced the function
12. y = (x + 1)2
13. y = x2 + 1
14. f(x) = sqrt(x) - 2
15. g(x) = sqrt(x - 2)
Answers 12-15
V. Composition (creating from other) of functions -- chapter 1, section 6
sum (f + g)(x)
difference (f - g)(x)
product (f · g)(x)
quotient (f ÷ g)(x)
composition (f o g)(x)= f(g(x))




Answer
2/22, 12. y = (x + 1)2 so y = h(i(x)) 
   h(x)			i(x)
x  --------->	 x + 1 --------->	(x + 1)2
   x + 1		x²
2/22, 13. y = x2 + 1 so y = i(h(x)) 
   i(x)			h(x)
x  --------->	 x2 --------->	x2 + 1
   x²			x + 1
2/22, 14. f(x) = sqrt(x) - 2 so f(x) = j(k(x)) 
   j(x)			k(x)
x  --------->	 sqrt(x) --------->	sqrt(x) - 2
   sqrt(x)		x - 2
2/22, 15. g(x) = sqrt(x - 2) so g(x) = k(j(x)) 
   k(x)			j(x)
x  --------->	 x - 2 --------->	sqrt(x - 2)
   x - 2		sqrt(x)




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