final jeopardy! - university of minnesotabrigh042/docs/1051/1051... · appendix 200. 2 22. 17. 2 2...

Final Jeopardy!Appendix Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5

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APPENDIX 200

Is the triangle with side lengths 17, 15, and 8 a right triangle? Why/Why not?

Appendix 200

2 2 2

2 2 217289 225

1564

289 28

8

9

c a b

= +

=

=

+

= +

If a right triangle, the Pythagorean theorem should hold:

Yes it is a right triangle

APPENDIX 400

Find the quotient and remainder

2 4

2

(1 )( 1)x

xx

x− ++ +

Appendix 4002 4

2

2

2 4 3 2

4 3 2

3 2

3 2

2

2

2 42

2

1)

1 0

(1 )(

1

2

(1 ) 1(

0 1

0 1

11

0

1)

xx

x x x xx x x

x

xx

x x

x x xx xx x

xx

x x

x x

x x xx

++ +

+ + + − + +

+ +

+ +

− − −

+ +

+ +

++

−=

− +

− −

−∴ = − +

+

APPENDIX 600

Solve for x

4( 2) 3 33 ( 3)

xx x x x− −

+ =− −

Appendix 600

2

2

2

8 3 9 34 5 6 0

5 5

4( 2) 3 3 0,33 ( 3)

4( 2) 3 3 3

4(4)( 6)

3 3 ( 3)4 ( 2) 3

5 121 5 11 32

( 3)

,2(4) 8 8 4

34

x xx x x x

x x xx x x x x xx

x xx x

x

x xx

− −+ = ⇒ ≠

− −− − −

+ =− − −− + −

− + − = −

− − =

± − − ± ±= = = = −

= −

APPENDIX 800

Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 A.M., each heading for Wildwood. One car’s average speed is 10 miles per hour more than the other’s. The faster car arrives at Wildwood at 11:00 A.M., a half an hour before the other car. What was the average speed of each car? How far did each travel?

Appendix 800

1 2

1 1 2 2

2 2

2 2

2

2 1

( 10)(3) (3.5)3 30 3.50.5 30

60 , 70

(70)(3) 210

dv d vtt

d dv t v tv vv v

vv mph v mphd vtd mi

= ⇒ =

==+ =+ ==

= === =

APPENDIX 1000

Rationalize and simplify:

( ) ( )( )

112 2 24

32 4

5 22 4

xy x y

x y

− +

Appendix 1000( ) ( )

( )

( ) ( )( )

( ) ( )( )

112 2 24

32 4

112 2 24

32 4

112 2 24

32 4

1 14 4

3 342

5 22 4

4 5 22 4 2 4

10 2 2 4 5 814

10 2 2 4 5 814

10 5

2

2 2 4 8

xy x y

x y

xy x y

x y

xy x y

x y

x

x y

y xy

− +

− + − = − + +

− + + − =

− + + − =

− + + −=

4 4

3 34

4

5 5

2

1 12

14

10 2 2 4 5 814

x

x

y

y

x y−

− + + −

=

CHAPTER 1 200

Find the distance between (-4,2) and (4,8)

Section 1.1

Chapter 1 200

( ) ( )

( ) ( )

2 2

2

2 1

2

1 2

4 ( 4) 8 2

100 10

d x x y y

d

d

= − −

= − −

=

+−

=

+

CHAPTER 1 400

Find the Midpoint of the line connecting(-4,2) and (4,8)

Section 1.1

Chapter 1 400

1 2 1 2,2 2

4 ( 4) 8 2,2 2

(0,5)

x x y yM

M

M

+ + =

+ − + =

=

CHAPTER 1 600

Find any intercepts and axes of symmetry

Section 1.2

2 4y x= +

Chapter 1 600

2

2

2

2

2

0 42 (0,2) & (0, 2)

:( ) 4

4 Yes, symmetric about x axisy:

( ) 44 No, not symmetric about x axis, hence

not sy

0 44 ( 4

mmetric about orig

0)

in

,x

xyy

xy x

y x

y xy x

= +=

= += ± ⇒ −

− = +

= +

= − +

= − +

− ⇒ −

Intercepts:

Axis of symmetry:

CHAPTER 1 800

With the given point and slope, find the equation of the line in slope-intercept form.

Section 1.3

3(2,4),4

P m= = −

Chapter 1 800

1 1

1 1

3(2,4) ( , );4

( )34 ( 2)4

3 114 2

P x y m

y y m x x

y x

y x

= = = −

− = −

− = − −

= − +

CHAPTER 1 1000

Find the standard form of the equation of a circle with endpoints of a diameter at (4,3) and (0,1).

Section 1.4

Chapter 1 1000( ) ( )2 1

22 1

2

2 2 2

2

2 2

2 2

1 2 1 2

20

202 2

( , ) , (2, 2)2 2

then the standard form of a circle is:( )

20( 2) ( 2)2

(

)

) ( 2) 5

(

2

diameter d x x y y

dradius r

x x y ycenter h k M

x h

x y

k

x

y r

y

= = − − =

= = =

+ + = = = =

−

− + −

− +

+

−

+ −

=

=

=

CHAPTER 2 200

If

Find the domain of f(x)*g(x)

Section 2.1

1 3( ) , ( )2 3

xf x g xx x

= =+ +

Chapter 2 200

1 3( ) , ( )2 3

3( )* ( )( 2)( 3)

( )* ( ) :{ | , 2, 3}

xf x g xx x

xf x g xx x

f x g x x x x

= =+ +

=+ +∈ ≠ − −

CHAPTER 2 400

Determine if the function is even, odd, or neither algebraically.

Section 2.3

3 25 2y x x−= +

Chapter 2 400

x x

100-x

100-x

To determine algebraically, substitute (-x) in for x:

As some signs change, but not all, we cannot conclude that it is even or odd. (Even=no signs change, Odd=all signs change) Hence it is neither.

3 2

3 2

3 2

5 2( ) 5( ) 2

5 2

xy x xy x

y xx

− +

= − − − +

−

=

− +=

CHAPTER 2 600

Locate all intercepts and graph the piecewise function

Section 2.4

( )

3 11 1

1 9

x

x

− ≤ −

= − < ≤ < <

x for xf x x for

x for

Chapter 2 600

Only intercept in the intervals is (0,0).

CHAPTER 2 800

List the transformation and graph each transformation, beginning with the standard graph

Section 2.4

( ) 3 1 8f x x= + −

Chapter 2 800

( ) 3 1 8f x x= + −

Shift one unit leftShift eight units downCompress by a factor of 3

CHAPTER 2 1000

An equilateral triangle is inscribed in a circle of radius r. Express the area within the circle, but outside the triangle as a function of the length of the triangle side, x and r

Section 2.5

Chapter 2 1000

2

2

2 2

34

(divide the equilateral triangle in half;

3/ 2, hypotenuse=x, find height= )2

34

circle

triangle

circle triangle

A r

A x

base x x

A A A r x

π

π

=

=

=

= − = −

CHAPTER 3 200

The monthly cost C, in dollars, for international calls on a certain cellular phone plan is given by the function

Where x is the number of minutes used.

(a) What is the cost if you talk on the phone for 50 minutes?

(b) Suppose that you budgeted yourself $60 per month for the phone. What is the maximum number of (whole) minutes that you can talk?

Section 3.1

( ) 0.38 5C x x= +

Chapter 3 200

( ) 0.38 5)(50) 24)

60 0.38 5144min

C x xaCb

xx

= +

=

= +=

CHAPTER 3 400

Determine the slope, y-intercept, where the function is increasing and decreasing and graph the function:

Section 3.1

4 10 52 22y x+ = −

Chapter 3 400

4 10 52 224 52 12

13 3

0 13 33 3 ,0

13 130 3

3 (0, 3)

y xy x

y x

x

x

yy

+ = −= −= −

= −

= ⇒

= −= − ⇒ −

Increasing on whole real line

CHAPTER 3 600

Graph the function by starting with a basic parabola and use transformations. Find all intercepts and axis of symmetry. Write in if necessary:

Section 3.3

2( )y a x h k= − +

2( ) 3 24 45f x x x− +=

Chapter 3 6002

2 2

2

2

2

24 45( ) 3( 8 15) 3( 8 16 1)( ) 3( 4) 3

Intercepts:0 3( 4) 3

1 45,3 (3,0) & (5,0)3(0 4) 345 (0,45)

Axis of Symmetry:24 4

2 6

( ) 3 xf x x x x xf x x

xx

xyy

bxa

f x x − +

= − + = − + −

= − −

= − −± = −= ⇒

= − −= ⇒

−= − = − =

=

CHAPTER 3 800

A special window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 16 feet, what dimensions will admit the most light?

Section 3.4

2.

34eq triangleA s=

x

x

x x

y y

Chapter 3 800

2

2 2

3 2 16382

34

3 3 3 68 84 2 4

Maximum obtained at vertex of parabola:8 16 3.7

2 3 6 3 62

2.5

3total height 5.72

P x y

y x

A xy x

A x x x x

bx fta

y ft

y x ft

= + =

= −

= +

−= + − = +

− −= − = = ≈

− −

≈

= + ≈

CHAPTER 3 1000

Solve the inequality

Section 3.5

2 165 02 4x x+ <

Chapter 3 10002

2

2

2

16 4025 40 16 0

8 16 05 254 05

4 40, 05 54 4 4,5 5 5

we can conclude that the graph is nonnegativem

25

eaning there are no values less than 0

xx x

x x

x

x

x x x

x

x

+ <

− + <

− + <

− <

− < − >

< > ⇒ =

∴

CHAPTER 4 200

Find the intercepts, where the function touches or crosses the x-axis, the number of turning points, and determine the end behavior of the function. Sketch the function.

Section 4.1

( ) ( 2)( 4)h x x x x= + +

Chapter 4 200

Intercepts:x: x=0, x=-2, x=-4y: y=0

Crosses at all x intercepts due to odd multiplicity

Number of Turning Points: 2

For x>>0, f(x) goes to infinity, for x<<0, f(x) goes to negative infinity

CHAPTER 4 400

Find the domain and any horizontal, vertical, and oblique asymptotes

Section 4.2

3

2

1( ) xG xx x

−=

−

Chapter 4 400

Domain: All reals except x=0,x=1, hole at x=1VA: x=0HA: none since (degree numerator)>(degree denominator)OA: y=-x-1 after long division

3 2 2 2

2

1 ( 1)( 1) ( 1)( 1) ( 1)( )(1 ) ( 1)

x x x x x x x x xG xx x x x x x x

− − + − − + − + −= = = = −

− − − −

CHAPTER 4 600

Go through the seven step process to obtain the graph of the function:

Section 4.3

2

2

2 7 15( )5

x xR xx x− −

=−

Chapter 4 600

CHAPTER 4 800

Go through the seven step process to obtain the graph of the function:

Section 4.3

3

2( )4

xR xx

=−

Chapter 4 800

CHAPTER 4 1000

Solve & Graph the solution set.

Section 4.4

( 2)( 1) 03

x xx

− −≥

−

Chapter 4 1000

( 2)( 1) 03

x xx

− −≥

−

( ,1) 0 0(1,2) 1.5 0(2,3) 2.5 0(3, ) 4 0

(1,2) (3, )

−∞ ⇒ ⇒≤⇒ ⇒≥⇒ ⇒≤

∞ ⇒ ⇒≥∴ ∪ ∞

Critical pts: 3, 2, 1Intervals:

CHAPTER 5 200

Find

Section 5.1

( ) and ( )2( ) ; ( )

3

f g x g f xxf x g x

x x= =

+

Chapter 5 200

2( ) ; ( )3

22 2( ) 2 2 3 2 33

2 2( 3) 6( ) 2

3

xf x g xx x

xf g xx xx

x xxg f x x x x

x

= =+

= = =+ + +

+

= = = +

+

CHAPTER 5 400

Find the inverse of the function.

Section 5.2

( ) 3 42

xg xx

− −=

−

Chapter 5 400( )

1 1

3 42

3 42

2 3 43 2 4

( 3) 2 42 4( )

3

xg x yx

yxy

xy x yxy y xy x x

xy g xx

− −

− −= =

−− −

=−

− = − −+ = −+ = −

−= =

+

CHAPTER 5 600

Solve the equation. Express any irrational solutions in exact form.

Sections 5.3 & 5.6

112 4 7 5 09x x+ + =

Chapter 5 600

( )

2

2

11 7 5 02 7 11 7

11 5 0(2 1)( 5) 0(2 7 1)(7 5) 02 7 1 0 or 7 5 0

17 or 7 52

1ln 7 ln or ln 7 ln 52

1ln ln 52 or ln 7 ln 7

no real solution

2 495 0

let 72

x x

x x

x

x x

x x

x x

yy y

x x

x x

yy

+ + =

•

+ + =+ + =

+ + =

+ = + =

= − = −

= − = −

− − = =

+ + =

=

CHAPTER 5 800

Write the expression as a single logarithm

Section 5.5

2 2

2log log2

2 3 7 64

x xx x

x x −

+ − + +− +

Chapter 5 800

2 2

2log log2

( 2)( 1) ( 6)( 1)log log( 2)( 2) 2

( 1) ( 2) 1log log( 2) ( 6) 6

2 3 7 64

x xx x

x x x xx x x

x xx

x

x

x

xx

− +

− − + + = − − + +

+ − +

− + −

+−

= = + + +

CHAPTER 5 1000

What will a $90,000 house cost 5 years from now if the price appreciation for homes over that period averages 3% compounded annually?

Section 5.7

Chapter 5 1000

5

90,00050.031

1

90,000(1.03)104,334.67

Approximately 104,334.67 dollars

nt

Ptrn

rA Pn

AA

====

= +

=≈