unit 4 day 7 quiz day #2 - honors icm ghhs · unit 4 day 7 quiz day #2. use g(x) for questions 1...
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Unit 4 Day 7
Quiz Day #2
Use g(x) for questions 1 – 6 and round to 3 decimal places. (Hint: You may need to Zoom Out!)2 36
( )7
xg x
x
1. Maximum: 2. Minimum:
3. Increasing: 4. Decreasing:
5. Domain: 6. Range:
Warm-Up Quiz #2 Day!
2
2
4 49( )
2 1 7
xf x
x x
Express the end behavior with correct limit notation.
8. 2
49 4( )
2 1 7
xh x
x x
9.
7. g(x) seen above
Use g(x) for questions 1 – 6 and round to 3 decimal places. (Hint: You may need to Zoom Out!)2 36
( )7
xg x
x
1. Maximum: 2. Minimum:
3. Increasing: 4. Decreasing:
5. Domain: 6. Range:
6.789 occurs at x = 3.394
( , 3.394] [10.606, ) [3.394, 7) (7, 10.606]
21.211 occurs at x = 10.606
Warm-Up Quiz #2 Day! ANSWERS
Warm Up Continued
( , 7) (7, ) ( , 6.789] [21.211, )
lim ( )x
g x
Warm-Up Quiz #2 Day! ANSWERS
2
2
4 49( )
2 1 7
xf x
x x
Express the end behavior.
8. 2
49 4( )
2 1 7
xh x
x x
9.
7. g(x) seen above
lim ( )x
g x
2 36( )
7
xg x
x
Top degree is bigger No HA look at ends on graph
4lim ( )7x
f x
Same degree HA is y = ratio of leading coeff.
4lim ( )7x
f x
lim ( ) 0x
h x
Bottom degree is bigger HA is y = 0
lim ( ) 0x
h x
Homework Questions?
Tonight’s Homework
Update your outline!
• Packet p. 6-7
5
( )limx
f x
( )limx
f x
0
( )limx
f x
( )limx
f x
Using the graph of f(x) below, find the following limits.
0
( )limx
f x
3
( )limx
f x
( 5)f
Practice Quiz #2 Day
5
( )limx
f x
( )limx
f x
0
( )limx
f x
( )limx
f x
Using the graph of f(x) below, find the following limits.
0
( )limx
f x
3
( )limx
f x
( 5)f
Practice Quiz #2 Day ANSWERS
1
5
0
DNE
3
1
More Practice for Quiz #2
Write an equation for the graphed rational function.
a. b.
Hole (-5, -1/2) Hole (3, 5)
Write an equation for the graphed rational function.
7. 8.
( 3)( 2)
( 3)
x xy
x
( 5)
( 5)( 3)
xy
x x
Hole (-5, -1/2) Hole (3, 5)
More Practice for Quiz #2: ANSWERS
Rational Functions Handout
Quiz Time!
• After you finish the quiz, complete the Rational Functions Handout
Use g(x) for questions a – d and round to 3 decimal places. 22 8
( )3
xg x
x
a. Maximum: c. Increasing:
b. Minimum: d. Decreasing:
3.056 occurs at x = .764 ( , 0.764] [5.236, )
[0.764, 3) (3,5.236]20.944 occurs at x = 5.236
Rational Functions Handout
Vertical
Asymptote(s)Analyze
Denominator
Horizontal
Asymptote(s)Analyze Degrees
of Polynomial
HOLES orRemovable
Point(s) of
Discontinuity
Simplify rational
by factoring
2 1( )
7
xf x
x
2
2
5( )
7 10
x xg x
x x
2
2
7 12( )
9
x xh x
x
22 5 3( )
3
x xf x
x
7x 2x 3x none
2y 1y 1y none
none5
( 5, )3
1
(3, )6
( 3, 7)
x-intercepts
set y = 0
y-intercepts
set x = 0
Domain(consider vertical
asymptotes and
x-value of hole)
Range(consider
horizontal
asymptote and
y-value of hole)
2 1( )
7
xf x
x
2
2
5( )
7 10
x xg x
x x
2
2
7 12( )
9
x xh x
x
22 5 3( )
3
x xf x
x
1( ,0)2
(0,0) (4,0) 1( ,0)2
1(0, )
7(0,0)
4(0, )
3 (0, 1)
( ,7) (7, ) ( , 2) ( 2, 5)
( 5, )
( , 3) ( 3,3)
(3, )
( , 3) ( 3, )
( ,2) (2, )
5( ,1) (1, )
3
5( , )3
1 1( , ) ( ,1)
6 6
(1, )
( , 7) ( 7, )
Find the
following limits
for the
functions
above.
Increasing:
Decreasing:
2 1( )
7
xf x
x
2
2
5( )
7 10
x xg x
x x
2
2
7 12( )
9
x xh x
x
22 5 3( )
3
x xf x
x
7lim ( )x
f x 5
lim ( )x
g x
lim ( )x
f x
2lim ( )
xg x
5
3
( , 3) ( 3,3)
(3, )
3lim ( )x
h x 3
lim ( )x
f x
1
6
( ,7) (7, ) 7