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