REVIEW PACKET REMINDERS
Graphing
Use your table of values to make the most accurate graph possible. Even when sketching, you
should have several key points.
Vertical / Horizontal Asymptotes: need to have x = 3 or y = 3. Just putting a number is
not correct.
X and Y intercepts: Notate using the coordinate point or x = ( y =). Don’t just put a
number.
Simplify all fractions as much as possible. Don’t convert to a decimal unless told to do so.
Decimal answers
need to go to 3 places
Show all steps.
Write down original formulas and/or problem.
Include any substitutions that you make.
Keep the equals sign! It doesn’t just disappear.
Acceptable:

0.9542
log 9

 3.170
0.3010
log 2
EX]
log2 9 =
EX]
Find the zeros of f(x) = 2x3 + 2x2 – 8x – 8
table)
Not acceptable:

log2 9  3.170
f(x) = 2x3 + 2x2 – 8x – 8
f(x) = 2x3 + 2x2 – 8x – 8
f(x) = 2x2(x + 1) – 8(x + 1)
The zeros are –2, 2, and –1.
f(x) = (2x2 – 8)(x + 1)
(I looked in my
f(x) =2(x2 – 4)(x + 1)
The zeros are –2, 2, and –1.
Domain/Range Notation: use interval notation. Infinity always has a soft ‘)’ bracket. Be
sure that you use the x or y coordinate that is appropriate.
Acceptable:

(- , )
Not acceptable:
ALL
[- , ]
All Real Numbers
All reals except x = 2
AR
All reals except 2
All reals except y = 3
All reals except 3
{x: x  3}
All reals but 3
If you have a hole in the graph, be sure you include it in the domain/range restriction.
End Behavior of Functions: Use the proper interval notation, and use your calculator to
determine relative max/min. Don’t just estimate. Be sure to use the x-coordinates!
EX]
f(x) = -x4 – 2x3 + 3x2 + 3x + 4 (problem 53 on packet)
(-2.0574, 10.026819)
Abs Max
(1.0000039, 6.9999961)
Rel Max
(-0.3882689, 3.3817903)
Rel Min
To describe the end behavior:
 You need to have both statements
As x  , f(x)  - 
As x  - , f(x)  - 
To describe the intervals on which f(x) is increasing / decreasing:
 Use interval notation, and be sure to use the x-coordinates!
F(x) is increasing on (- , -2.0574) and (-0.3882689, 1.0000039)
F(x) is decreasing on (-2.0574, -0.3882689) and (1.0000039, )
WHAT TYPE OF NOTATION WILL WE BE USING THIS YEAR?
INTERVAL NOTATION!!