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
====
= +
=≈