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

200

400

600

800

1000

200

400

600

800

1000

200

400

600

800

1000

200

400

600

800

1000

200

400

600

800

1000

200

400

600

800

1000

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

====

= +

=≈