Final Jeopardy!
Appendix
Ch. 1
Ch. 2
Ch. 3
Ch. 4
Ch. 5
200
200
200
200
200
200
400
400
400
400
400
400
600
600
600
600
600
600
800
800
800
800
800
800
1000
1000
1000
1000
1000
1000
A PPENDIX
200
Is the triangle with side lengths 17, 15, and 8 a right
triangle? Why/Why not?
Appendix
200
If a right triangle, the Pythagorean theorem should hold:
c = a +b
2
2
2
2
17=
152 + 82
289
= 225 + 64
289 = 289
Yes it is a right triangle
A PPENDIX
400
Find the quotient and remainder
(1 − x + x )
2
( x + x + 1)
2
4
Appendix
(1 − x 2 + x 4 )
=
2
( x + x + 1)
x2 − x + 1
x 2 + x + 1 x 4 + 0 x3 − x 2 + 0 x + 1
x 4 + x3 + x 2
− x3 − 2 x 2 + 0 x + 1
− x3 − x 2 − x
x2 + x + 1
x2 + x + 1
0
(1 − x 2 + x 4 )
∴ 2
= x2 − x + 1
( x + x + 1)
400
A PPENDIX
Solve for x
4( x − 2) 3
−3
+ =
x −3
x x( x − 3)
600
Appendix
600
4( x − 2) 3
−3
=
+
⇒ x ≠ 0,3
x −3
x x( x − 3)
x 4( x − 2) x − 3 3
−3
+
=
x x −3
x − 3 x x( x − 3)
4 x( x − 2) + 3( x − 3) = −3
4 x 2 − 8 x + 3x − 9 =−3
4 x2 − 5x − 6 =
0
5 ± 52 − 4(4)(−6) 5 ± 121 5 ± 11
3
x=
=
=
= 2, −
2(4)
8
8
4
A PPENDIX
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
d
v = ⇒ d = vt
t
d1 = d 2
v1t1 = v2t2
(v2 + 10)(3) =
v2 (3.5)
3v2 + 30 =
3.5v2
0.5v2 = 30
=
=
v2 60
mph, v1 70mph
d = vt
=
= 210mi
d (70)(3)
800
A PPENDIX
1000
Rationalize and simplify:



1
1

2 2 2
4
xy
x
5 − 2  ( ) ( y )
 
3
2 + 4 
2
4
x
y
(
)






Appendix
1
1

2 2 2 
 5 − 2   ( xy ) 4 ( x y ) 

 
3

2
+
4
2


( x y ) 4 

1
1

2 2 2 
 − 2 + 4   5 − 2   ( xy ) 4 ( x y ) 
= 
 
 
3

−
+
+
2
4
2
4
2



4

( x y)


1
1

2 2 2
4
 − 10 + 2 2 + 4 5 − 8   ( xy ) ( x y )
= 
 
3
14
2


( x y )4

 14 14

 − 10 + 2 2 + 4 5 − 8   x y xy 
= 
 
3
3

14


 x2 y4 


 54 54 
 − 10 + 2 2 + 4 5 − 8   x y 
= 
  3 3 
14

 x2 y4 


 − 10 + 2 2 + 4 5 − 8   −41 12 
= 
  x y 
14



1000





C HAPTER 1
Find the distance between (-4,2) and (4,8)
Section 1.1
200
Chapter 1
200
d=
( x2 − x1 ) + ( y2 − y1 )
2
d=
( 4 − (−4) ) + (8 − 2 )
2
d = 100 = 10
2
2
C HAPTER 1
400
Find the Midpoint of the line connecting(-4,2) and
(4,8)
Section 1.1
Chapter 1
 x1 + x2 y1 + y2 
M =
,

2
2


 4 + (−4) 8 + 2 
M =
,

2
2 

M = (0,5)
400
C HAPTER 1
Find any intercepts and axes of symmetry
y = x+4
2
Section 1.2
600
Chapter 1
Intercepts:
0= x + 4
x = −4 ⇒ (−4, 0)
y 2= 0 + 4
y =±2 ⇒ (0, 2) & (0, −2)
Axis of symmetry:
x:
(− y ) 2 =x + 4
y 2= x + 4 Yes, symmetric about x axis
y:
y 2 =(− x) + 4
y 2 =− x + 4 No, not symmetric about x axis, hence
not symmetric about origin
600
C HAPTER 1
800
With the given point and slope, find the equation of
the line in slope-intercept form.
3
P = (2, 4), m = −
4
Section 1.3
Chapter 1
3
P = (2, 4) = ( x1 , y1 ); m = −
4
y − y1 = m( x − x1 )
 3
y − 4 =  −  ( x − 2)
 4
3
11
y=
− x+
4
2
800
C HAPTER 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
diameter ==
d
( x2 − x1 ) + ( y2 − y1 ) =20
2
radius= r=
d
=
2
2
20
2
 x + x y + y2 
center
= (h, k=
=  1 2, 1
=
) M
 (2, 2)
2 
 2
then the standard form of a circle is:
( x − h) 2 + ( y − k ) 2 = r 2
 20 
( x − 2) + ( y − 2) = 

2


( x − 2) 2 + ( y − 2) 2 = 5
2
2
2
C HAPTER 2
If
1
3x
=
f ( x) =
, g ( x)
x+2
x+3
Find the domain of f(x)*g(x)
Section 2.1
200
Chapter 2
1
3x
=
f ( x) =
, g ( x)
x+2
x+3
3x
f ( x) * g ( x) =
( x + 2)( x + 3)
f ( x) * g ( x) :{x | x ∈ , x ≠ −2, −3}
200
C HAPTER 2
400
Determine if the function is even, odd, or neither
algebraically.
y = x − 5x + 2
3
Section 2.3
2
Chapter 2
400
100-x
To determine algebraically, substitute (-x) in for x:
x
y = x3 − 5 x 2 + 2
x
y =(− x)3 − 5(− x) 2 + 2
100-x
y = − x3 − 5 x 2 + 2
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.
C HAPTER 2
600
Locate all intercepts and graph the piecewise
function
 − x 3 for x ≤ −1

=
f ( x )  x for − 1 < x ≤ 1

 x for 1 < x < 9
Section 2.4
Chapter 2
Only intercept in the
intervals is (0,0).
600
C HAPTER 2
800
List the transformation and graph each transformation,
beginning with the standard graph
f ( x)= 3 x + 1 − 8
Section 2.4
Chapter 2
f ( x)= 3 x + 1 − 8
Shift one unit left
Shift eight units down
Compress by a factor of 3
800
C HAPTER 2
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
1000
Chapter 2
Acircle = π r
1000
2
3 2
Atriangle =
x
4
(divide the equilateral triangle in half;
3
base = x / 2, hypotenuse=x, find height=
x)
2
3 2
2
A=
Acircle − Atriangle =
x
πr −
4
C HAPTER 3
200
The monthly cost C, in dollars, for international calls
on a certain cellular phone plan is given by the
function
C
=
( x) 0.38 x + 5
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
Chapter 3
C
=
( x) 0.38 x + 5
a)
C (50) = 24
b)
=
60 0.38 x + 5
x = 144min
200
C HAPTER 3
400
Determine the slope, y-intercept, where the
function is increasing and decreasing and graph
the function:
4 y + 10 = 52 x − 22
Section 3.1
Chapter 3
4 y + 10 = 52 x − 22
=
4 y 52 x − 12
y 13 x − 3
=
Increasing on whole real
line
=
0 13 x − 3
3
3 
x
=
⇒  ,0
13  13 
y= 0 − 3
y =−3 ⇒ (0, −3)
400
C HAPTER 3
600
Graph the function by starting with a basic parabola
and use transformations. Find all intercepts and
axis of symmetry. Write in y = a( x − h)2 + k if
necessary:
f ( x) = 3 x 2 − 24 x + 45
Section 3.3
Chapter 3
f ( x) = 3 x 2 − 24 x + 45
f ( x)= 3( x 2 − 8 x + 15)= 3( x 2 − 8 x + 16 − 1)
f ( x) = 3( x − 4) 2 − 3
Intercepts:
0 = 3( x − 4) 2 − 3
±1 = x − 4
=
x 5,3 ⇒ (3, 0) & (5, 0)
y = 3(0 − 4) 2 − 3
=
y 45 ⇒ (0, 45)
Axis of Symmetry:
−24
b
−
=
−
=
x=
4
2a
6
600
C HAPTER 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?
3 2
Aeq.triangle = s
4
x
x
x
Section 3.4
y
y
x
Chapter 3
P = 3 x + 2 y =16
3
y= 8 − x
2
3 2
= xy +
A
x
4
 3 3
 3 −6 2
2
−  =8 x + 
A =8 x + x 
 x
 4 2
 4 
Maximum obtained at vertex of parabola:
b
−8
−16
x=
−
=
=
≈ 3.7 ft
2a
3 −6
3 −6
2
y ≈ 2.5 ft
3
y+
x ≈ 5.7 ft
total height =
2
800
C HAPTER 3
Solve the inequality
25 x + 16 < 40 x
2
Section 3.5
1000
Chapter 3
1000
25 x 2 + 16 < 40 x
25 x 2 − 40 x + 16 < 0
8
16
2
x − x+
<0
5
25
2
4

x
−

 <0
5

4
4
x − < 0, x − > 0
5
5
4
4
4
x < ,x > ⇒ x =
5
5
5
∴ we can conclude that the graph is nonnegative
meaning there are no values less than 0
C HAPTER 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.
h( x) =x( x + 2)( x + 4)
Section 4.1
Chapter 4
Intercepts:
x: x=0, x=-2, x=-4
y: 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
200
C HAPTER 4
400
Find the domain and any horizontal, vertical, and
oblique asymptotes
x −1
G ( x) =
2
x−x
3
Section 4.2
Chapter 4
G ( x)
400
x3 − 1 ( x − 1)( x 2 + x − 1) ( x − 1)( x 2 + x − 1)
( x 2 + x − 1)
= = −
2
x−x
x(1 − x)
− x( x − 1)
x
Domain: All reals except x=0,x=1, hole at x=1
VA: x=0
HA: none since (degree numerator)>(degree denominator)
OA: y=-x-1 after long division
C HAPTER 4
600
Go through the seven step process to obtain the
graph of the function:
2 x 2 − 7 x − 15
R( x) =
x2 − 5x
Section 4.3
Chapter 4
600
C HAPTER 4
800
Go through the seven step process to obtain the
graph of the function:
3
x
R( x) = 2
x −4
Section 4.3
Chapter 4
800
C HAPTER 4
Solve & Graph the solution set.
( x − 2)( x − 1)
≥0
x−3
Section 4.4
1000
Chapter 4
( x − 2)( x − 1)
≥0
x−3
Critical pts: 3, 2, 1
Intervals:
(−∞,1) ⇒ 0 ⇒≤ 0
(1, 2) ⇒ 1.5 ⇒≥ 0
(2,3) ⇒ 2.5 ⇒≤ 0
(3, ∞) ⇒ 4 ⇒≥ 0
∴ (1, 2) ∪ (3, ∞)
1000
C HAPTER 5
Find
f  g ( x) and g  f ( x)
x
2
=
f ( x) =
; g ( x)
x+3
x
Section 5.1
200
Chapter 5
x
2
f ( x) =
=
; g ( x)
x+3
x
2
2
2
x
f =
g ( x) =
=
2
2 + 3x  2 + 3x

+ 3 x

x
 x 
2
2( x + 3)
6
g  f ( x)=
=
= 2+
x
x
x
x+3
200
C HAPTER 5
Find the inverse of the function.
−3 x − 4
g ( x) =
x−2
Section 5.2
400
Chapter 5
−3 x − 4
g ( x )= y=
x−2
−3 y − 4
x=
y−2
xy − 2 x =
−3 y − 4
xy + 3 y = 2 x − 4
y ( x + 3) = 2 x − 4
2x − 4
−1
−1
y
g=
=
( x)
x+3
400
C HAPTER 5
600
Solve the equation. Express any irrational solutions
in exact form.
249 + 117 + 5 =
0
x
Sections 5.3 & 5.6
x
Chapter 5
249 x + 117 x + 5 =
0
2 • 7 2 x + 117 x + 5 =
0
let y = 7 x
2 y 2 + 11 y + 5 =
0
(2 y + 1)( y + 5) =
0
(27 x + 1)(7 x + 5) =
0
x
+5 0
2=
7 x + 1 0 or 7=
1
7x =
− or 7 x =
−5
2
1
ln − or x ln 7 =
ln − 5
x ln 7 =
2
 1
ln  − 
ln ( −5 )
2

or x
x =
=
ln 7
ln 7
no real solution
600
C HAPTER 5
800
Write the expression as a single logarithm
 x2 + 2 x − 3 
 x2 + 7 x + 6 
log 
 − log 

2
 x −4 
 x+2 
Section 5.5
Chapter 5
800
 x2 + 2x − 3 
 x2 + 7 x + 6 
log 
 − log 

2
 x −4 
 x+2 
 ( x − 2)( x − 1) 
 ( x + 6)( x + 1) 
log 
 − log 

x+2


 ( x − 2)( x + 2) 
 ( x − 1) ( x + 2) 
 x −1 
=

log

 log 

 x+6
 ( x + 2) ( x + 6) 
C HAPTER 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
P = 90, 000
t =5
r = 0.03
n =1
nt
 r
=
A P 1 + 
 n
A = 90, 000(1.03)5
A ≈ 104,334.67
Approximately 104,334.67 dollars
1000