day 6 review jeopardy
TRANSCRIPT
Jeopardy Game
For Calculus Review
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Domain & Range
Limits at #Limits @ Infinity
Limits of Piecewise
Discontinuity
$100$100
Find the Domain and Range:
f(x)=4x3-2x+8
Find the Domain and Range:
f(x)=4x3-2x+8
$100$100
D: (-∞, ∞)
R: (- ∞, ∞)
D: (-∞, ∞)
R: (- ∞, ∞)
$200$200
Identify the domain and range:
f(x)=4x2-5
Identify the domain and range:
f(x)=4x2-5
$200$200
D: (- ∞, ∞)
R:[-5, ∞)
D: (- ∞, ∞)
R:[-5, ∞)
$300$300
Identify the domain and range
g(x)=
Identify the domain and range
g(x)= 5x
$300$300
D: [-5, ∞)
R: [0, ∞)
D: [-5, ∞)
R: [0, ∞)
$400$400
Identify the domain and range:
h(x)=
Identify the domain and range:
h(x)=2
3
16
x
x
$400$400
D: (- ∞,-4)U(-4,4)U(4, ∞)
R: (- ∞, ∞)
D: (- ∞,-4)U(-4,4)U(4, ∞)
R: (- ∞, ∞)
$500$500
Identify the domain and range:
f(x)=
Identify the domain and range:
f(x)=2
x
x
$500$500
D: [0,2)U(2, ∞)
R: (-∞, ∞)
D: [0,2)U(2, ∞)
R: (-∞, ∞)
$100$100
4lim3 2x
x
$100$100
1010
$200$200
3lim8x
$200$200
88
$300$300
2
6
36lim
6x
x
x
$300$300
1212
$400$400
3
5lim
3x
x
x
$400$400
-∞-∞
$500$500
24
2lim
4x
x
x
$500$500
-.167 or -1/6 -.167 or -1/6
$100$100
lim3 5x
x
$100$100
∞∞
$200$200
4
3 6
4 5lim
5x
x x
x x
$200$200
00
$300$300
5 3lim
6 2x
x
x
$300$300
5
6
$400$400
4 2
2
3 5lim
6 7x
x x
x
$400$400
-∞-∞
$500$500
2
4
3 5lim
16 3x
x x
x x
$500$500
¾¾
$100$100
2
5, 5( )
, 5
x if xf x
x if x
5lim ( )xf x
$100$100
DNEDNE
$200$200
3 2, 3( )
14, 3
x if xg x
x if x
3lim ( )x
g x
$200$200
-11-11
$300$300
2
4, 2
2( )8
, 24
xx
xh x
xx
2lim ( )xh x
$300$300
-∞-∞
$400$400
2
3, 2
( ) 1, 2 5
21, 5
if x
f x x if x
x if x
5lim ( )xf x
$400$400
44
$500$500
2
3, 6
( ) 93, 6
xif x
g x xif x
3lim ( )xg x
$500$500
1/6 or .1671/6 or .167
$100$100
Determine if the function is continuous. If not identify
the discontinuities.
f(x)= x2–3x+7
Determine if the function is continuous. If not identify
the discontinuities.
f(x)= x2–3x+7
$100$100
CONTINUOUSCONTINUOUS
$200$200
Determine if the function is continuous. If not identify
the discontinuities.
Determine if the function is continuous. If not identify
the discontinuities.
3 2( )
6
xf x
x
$200$200
Discontinuous
Asymptote at x= -6
Discontinuous
Asymptote at x= -6
$300$300
Determine if the function is continuous. If not identify
the discontinuities.
Determine if the function is continuous. If not identify
the discontinuities.3
, 10( ) 5
2, 10
xif x
f x xx if x
$300$300
Discontinuous
Asymptote at x=5
Jump at x=10
Discontinuous
Asymptote at x=5
Jump at x=10
$400$400
Identify any discontinuities, if possible create a
continuous function.
Identify any discontinuities, if possible create a
continuous function.2 5 6
( )1
x xf x
x
$400$400
Discontinuous
Hole at (1,7)
Discontinuous
Hole at (1,7)2 5 6
, 1( ) 1
7 , 1
x xif x
g x xif x
$500$500
Find the values of a and b that make g(x) continuousFind the values of a and b that make g(x) continuous
2
3 10, 3
( ) , 3 5
6 13, 5
x if x
g x ax b if x
x if x
$500$500
3(-3)+10=1
a(-3)2+b=9a+b
9a+b=1
a(5)2+b=25a+b
6(5)-13=17
25a+b=17
9a+b=125a+b=17-9a-b=-116a=16
a=19(1)+b=1
9+b=1b=-8
f(x+h) - f(x)h
Simplify the following given f(x) = 3x2 - 6