NEW Review Guide (With Answers).notebook June 04, 2018
Answer Key
NEW Review Guide (With Answers).notebook June 04, 2018
RealIntegerInteger
Integer
Integer
Natural
Natural
Whole
Whole
Rational
RationalRational
Rational
Irrational
Irrational
Rational
Rational
Rational
RealRealRealReal
RealReal
RealReal
AlwaysSometimes
AlwaysNever
11
102 2 = 100 |102 + 2||104| = 104
10 2 = 12 |40|40
(9)9
the opposite of 3 squared 9 3 3
9negative 3 squared
(9)9
32 12 14 7
99 105 5 6
NEW Review Guide (With Answers).notebook June 04, 2018
110 + 85 = x25 = x 25 feet below sea level
22 (8) = x30 = x 30 degree difference
16 + 9 = x7 = x
7
6 + 3 106 + 30 36
8 6 + 248 + 2 50
25 (9 4) 25 5
=
=
5
213 (5)
31
2
6 + 3 +
3 + 5
(6)2 + (5)3
36 + 1255 6 2 5
36 125161
4030 + 10
3 + 1
4
undefined undefinedzero zero022
220
NEW Review Guide (With Answers).notebook June 04, 2018
5x x2y 3y 75x x 2y 3y5 1 2 3
7
1
4a 10c 8 2a 74a 2a 8 74 10 28 7
21 28x + 8 + 10x 18x 13 10 18x 12 + 9x 9x 2
19x + 24 + 9x 13 19x 2610x + 11 12x 17 + 7x 9
1
15x 12y + 34 167x 140 19x 5
12x 145 15x 12y + 18
3 2x + 5 + x 7 5
2
4x 2
2 3
1 4x y x y 1
2 2 5
3 20 x 1 y 1
6
NEW Review Guide (With Answers).notebook June 04, 2018
1 ±13 -4
43 -5
4 5 10 11 6 7
12 13
NEW Review Guide (With Answers).notebook June 04, 2018
√ √4
-5 16 7
√-20 7√11
-33 -3 121
√-3 121
√ √3
9 7 x4
√3x2 7√
x2
√ √5
x 25 6 x4 x1
√5x3 6x
√x2
√ √ √3
-3 9 5 y4 y1
√-9y2 5y√
y2
√ √2
-2b 4 34 b8
√-4b5 34
√b4
√
√√ √6 36 5
√6 5
180 √
√12
2 144 2 √24 22 288
√√
√7
-4 49 6 √-28 6-4 294
√
√60n3
√ √2
4 15 n2 n1 √2n 15n
√n
√√-6 2240x6
√ √8
-6 64 35 x6
√-48x3 35√
x3 34√240x6
√ √416 15 x6
√3x3 15√
x3
34
36
49
√√
= 67 √ √
2 4 2
3 √√ √
x2
49 x4 x1
√5x
7x2 x
25 x2
√√x5
7
= √3
2 2 √
√ √y3
225 y6 y1
√8x2
15y3 y
64 x4
√√ x28
15
12 3 √
√ √√4
8 3 + 2 16 3
3 11 -3 7√ √1 1
√ √8 3 + 8 3 16 3 √
√ √3
3 4 5 + 2 9 5
√ √6 5 + 6 5 12 5 √
√ √ √2
√5
4 3 - 7 25 3
√ √2 3 - 35 3 -33 3 √
√ √2
NEW Review Guide (With Answers).notebook June 04, 2018
24 s7 a5b2
1 32
= 19
1 41
= 14
41= 1 x8
x8 =
29 46 105
k9 a6c7 10w5x5
21x6 16y7 30x9
42y416w10z6
6x3y7
a8c4 x6y8 m6n9
16x4y4 27x12y21 100x2y10
34 = 81 1 26
= 1 64
26 = 86 3n3
4x6 9y5 5x3y2
7w4m2
NEW Review Guide (With Answers).notebook June 04, 2018
15 x
2y8 1 5x2y8
13 w
4x2 x2 3w4
2.204 x 1096.59 x 1034.7338 x 106
8.331 x 10-42.9 x 10-1 5.71 x 10-6
0.335
67 61,000 1600
0.0000291 0.0000008651
NEW Review Guide (With Answers).notebook June 04, 2018
>>>
>
6 102 48 109
4.8 1010
5 102 11 1012
1.1 1013
NEW Review Guide (With Answers).notebook June 04, 2018
polynomial 5x3 3x2 + 14x + 2 3
binomial
polynomial
polynomial
trinomial
monomial
9z3 2z
7y5 + 3y2 + 2y + 2
3
5
5
2
2
7x5 + x3 2x2 + 4
5x2 + 2x 7
3x2
x2 - 7x - 20 5x4 - 15x3 + 10x2 -6y + 21y2 - 24 - 5y
21y2 - 11y - 24
NEW Review Guide (With Answers).notebook June 04, 2018
4x + 16 - 3x4 + 9x2 - 2x + 5 n2 + 5n + 6n 2x2 + 3x + 4x2 - x + 1
-3x4 + 9x2 + 2x + 21 n2 + 11n 6x2 + 2x + 1
2x + 4y - 1 - x - 7 - 6yx - 2y - 8
5x2 + 12x - 17 - 13 + 4x2 - 8x9x2 + 4x - 30
3x + 10 + 6x - 159x - 5
x2 + 9x - 5x2 + 3x-4x2 + 12x
-5x2 + 8x + 12 + 3x2 - 4x + 8
-2x2 + 4x + 20
6x2 - 11x - 17 - 9x2 + 8x + 12
-3x2 - 3x - 5
5x + 3 + 2x + 5x + 3 + 2x
14x + 6 units 8y - 4 + 9y - 5 + 3y
20y - 9 units
NEW Review Guide (With Answers).notebook June 04, 2018
x2 - 3x + 2 + x2 - 3x + 2 + 3x - 7 + 3x - 72x2 - 10 units
5x3 + 3y + 5x3 + 3y + 5x3 + 3y15x3 + 9y units
x5y - x2y2 -112m2n + 64mn2 -24mn x3z4 - 5x3z2
x3a5 - 8xa4ca5x3 - 8a4cx
8x5y2 + 60x2yz - 28x2y 3x3y2 + 6x4 + 3x3z
2x + 2x + 5x 2 + 5x 214x 4
Perimeter = 14x 4 feet
A = 2x (5x 2)
A = lw
Area = 10x2 4x feet2
P = add up all sides
A = 10x2 4x
x2 + 1x + 5x + 5x2 + 6x + 5
y2 7y + 4y 28y2 3y 28
x2 + 3x 10x 30x2 7x 30
a2 5a 4a + 20a2 9a + 20
2x2 2x + 6x 62x2 + 4x 6
12x2 + 2x + 12x + 212x2 + 14x + 2
25x2 35x + 35x 4925x2 49
6x2 + 18x + 12x + 366x2 + 30x + 36
4x3 + 12x2 8x + x2 + 3x 2
4x3 + 13x2 5x 2
NEW Review Guide (With Answers).notebook June 04, 2018
GCF: 5 GCF: 3x GCF: 4 GCF: 4y
x (1 y) 5 (3m + 10) 6 (3n + 4) 7y (3x 4)
2x (2x3 11x + 9) 7x2 (3x3 + 5x + 7)
c3 (2c2d4 3c + 4) y (23y9 46y6 + 68y + 10)
x2 + 6x + 6x + 36
(x + 6) (x + 6)
x2 + 12x + 36
(x 6) (x 6)
x2 6x 6x + 36x2 12x + 36
x3 + 4x2 + 2x + 3x2 + 12x + 6x3 + 7x2 + 14x + 6
3x + 1 5a2 + ab 2b6z2 3y + 2z
4 + 5vw 4w5vw 4w + 4
x2 2x xy2z
2z + 6z2 3y
xy2z + x2 2x
NEW Review Guide (With Answers).notebook June 04, 2018
Same Signs both positive Same Signs both negativeDifferent Signs Bigger positivemult. to 40, add to 14
(x + 10) (x + 4) mult. to 24, add to 5(x + 8) (x 3)
mult. to 20, add to 9(x 5) (x 4)
Same Signs both positive Same Signs Both negativemult. to 15, add to 16
(x + 15) (x + 1)mult. to 14, add to 9(x 7) (x 2)
mult. to 24, add to 11
(x 8) (x 3)
Same Signs both negative
4 (6x 5)24x 20 Perimeter = 24x 20 units
A = (6x 5)2A = s2
Area = 36x2 60x + 25 units2
P = add up all sides
A = 36x2 30x 30x + 25A = (6x 5) (6x 5)
36x2 60x + 25 36(2)2 60(2) + 25 36(2)2 60(2) + 25 144 120 + 25
49
The puppy will have 49 square feet of space to play.
NEW Review Guide (With Answers).notebook June 04, 2018
2x 2x2x 7 = 15
+ 7+ 72x = 222 2 x = 11
22c + 88 = 22 88 88
22 22c = 5
22c = 110
20x + 16 2x = 14x 2822x + 16 = 14x 28
8 8x = 5.5
8x = 44
. . .
+12+ 12
x = 35
37
73
x = -15 73
2x - 53
= 5 (3)3
2x - 5 = 15+ 52x = 20
+ 5
2 2x = 10
4x + 8 = 2x 16 2x 2x
6x + 8 = 16 8 86x = 24-6 -6x = 4
NEW Review Guide (With Answers).notebook June 04, 2018
0.4y 3.6 = 0.3y + 1.23 (x + 2) = 7 (x 2)
4 4x = 5
4x = 20
. . .
+1.8x+1.8x5x 7.1 = 6.8+ 7.1 +7.15x = 13.95 5x = 2.78
3x + 6 = 7x 140.1
x = 48
0.1y = 4.8
. . .
0.1
3x + 7 = 3x + 6 3x
ContradictionNo Solution
3x7 ≠ 6
2x + 9 = 2x + 8 + 12x + 9 = 2x + 9 2x 2x
9 = 9Identity
Infinite Solutions
√x2 = 49√x = ± 7
x2 = 81-10 -10
√x2 = 81√ x = ± 92x2 = 50
+5+5
2 2√x2 = 25√
x = ± 5
x = 2q
3x = 6q3 3
x = 6a
5x = 30a
. . .
5 5
5 r - 10y = x
r = 5x + 10yr - 10y = 5x y - z = 2x
2 y - z = x
Let c = the # of cups $7.50 + $2.50c = $12.50
7.50 + 2.50c = 12.50c = 2
You can buy 2 cups of food.
NEW Review Guide (With Answers).notebook June 04, 2018
Let c = the # of chocolates $3c - $45 = $105
3c - 45 = 105c = 50
You must sell 50 chocolates.
Let w = the # of weeks $100 + $20w = $280
100 + 20w = 280
w = 9It will take you 9 weeks.
Let x = cost of 1st item Let x + 8 = cost of 2nd item x + x + 8 = $130
x + x + 8 = $1302x + 8 = $130
x = 61
The items cost $61 and $69.
Let n = 1st odd integer Let n + 2 = 2nd odd integer n + n + 2 = 84
n + n + 2 = 842n + 2 = 84
n = 43The integers
are -43 and -41.
NEW Review Guide (With Answers).notebook June 04, 2018
0.5x + 6 < 9x < 6
60 -5 0
x ≤ -5
x ≤ -1
-1 0
4x 3 > 21
x > 6
60
5n + 3 ≥ 382x 4 > 17
2 + 7 ≤ 40 x
e ≤ 3600a ≥ 45a ≤ 50
NEW Review Guide (With Answers).notebook June 04, 2018
Let x = # of tickets 12x + $2157 ≥ $4500
12x + 2157 ≥ 450012x ≥ 2343
x ≥ 195.25
They must sell at least
196 tickets.
Let x = # of boxes 3x + $12.75 ≤ $38
3x ≤ 25.25x ≤ 8.41666...
They can buy at most8 boxes.
3x + 12.75 ≤ 38
NEW Review Guide (With Answers).notebook June 04, 2018
Let x = # of tickets 12x + $2157 ≥ $4500
12x + 2157 ≥ 450012x ≥ 2343
x ≥ 195.25
They must sell at least
196 tickets.
Let x = # of boxes 3x + $12.75 ≤ $38
3x ≤ 25.25x ≤ 8.41666...
They can buy at most8 boxes.
3x + 12.75 ≤ 38
0.5 pounds /week$20 /ticket
16x = 9
16x = 1441612
x = 2
12x = 2512
12 1
50 n =1 3.2 1x = 160
1n = 1601 The actual distance between
the cities is 160 km.
Let n = the actual distance
NEW Review Guide (With Answers).notebook June 04, 2018
14 ounces
10 teaspoons2 1
= 0.75 teaspoons/ ounce
6 laps
4 minutes2 1
= 0.75 minutes/ lap
20 pounds$14.99 = 0.7495 $0.75/ pound
50 pounds$37.99 = 0.7598 $0.76/ pound
The 20 pound bag is a better buy because it costs less per pound.
2 DVD's$26.50 = 13.25 $13.25/ DVD
3 DVD's$40.00 = 13.3333... $13.33/ DVD
The 2 pack of CD's is a better buy because it
costs less per DVD.
0.75 lb$6 $8/ pound
1 lb$8.50 $8.50/ pound
A
B
0.25 lb$2.25 $9/ poundC
4 oz = 0.25 lb
NEW Review Guide (With Answers).notebook June 04, 2018
4 24 324
c = 4ty = 4x
NEW Review Guide (With Answers).notebook June 04, 2018
y
x
The graph repersents a proportional relationship because it is a straight line that passes through the origin. (0, 0)
28
y = 2x b = 2c36
b = 2c b = 2 18b = 36
y = 0.99x c = 0.99a
21
n = 121.9047 ...
21n = 25602121 512 = 5 n You would expect
about 122 people to have green eyes.
Let n = # of people expected with green eyes
NEW Review Guide (With Answers).notebook June 04, 2018
n = 4.5731 ...
1230n = 562512301230 375 = 15 n
You would expect about 5 cars to have headlight problems.
1230
Let n = # of cars expected with headlight problems
y 9
6 15
=
3.6 = y
54 = 15y15 15
3.6 ft
little big x
9 28 12
=
21 = x
252 = 12x12 12
21 m
big little
NEW Review Guide (With Answers).notebook June 04, 2018
0.875 87.5%
215% 220 3
2043OR
0.0425 1
0.666.6 %66 %3
2 OR
2%50 1
0.2825 7
p 192
25 100
=48 = p
4800 = 100p100100 Mary earned $48 commission.
Let p = amount of commission
p 85
15 100
=12.75 = p
1275 = 100p100100 Jenny paid $72.25 for the boots.
discount = $12.75Sale Price = 85 - 12.75 = 72.25
Let p = amount of discount
p 99.50
7.5 100
=
7.4625 = p
746.25 = 100p100100
The bicycle costs $106.96.
tax = $7.46Total = 99.50 + 7.4625 = 106.9625
Let p = amount of tax
NEW Review Guide (With Answers).notebook June 04, 2018
p 350
12 100
= 42 = p
4200 = 100p100100 42 people will
win a door prize.Let p = # of people who will win
p 22
5.25 100
= 1.155 = p
bill = 22+1.155 = 23.155
p 23.155
15 100
=
3.47325 = p
Total = 23.155 + 3.47325= 26.62825
= $26.63
Let p = tax Let p = tip
Find the discount first:
n 300
= 30 100
90 = n$300 - $90 = $210
Now find the sales tax on the discounted price:
n 210
= 8 100
16.8 = n
Let n = taxLet n = discount
discount = $90tax = $16.80
Total = 210 + 16.80= 226.80
= $226.80
I = PRTI = (1750)(0.0875)(2.5)I = 382.8125I = $382.81
Total = P + IT = 1750 + 382.81
Total = $2132.81
She started her bank account with $800.
I = PRT147 = P (0.1225)(1.5)147 = 0.18375P
0.18375 0.18375
800 = P
65 x
70 100
=92.8571 . . . = x
6500 = 70x7070 The original price
is $92.86.
Let x = original price
NEW Review Guide (With Answers).notebook June 04, 2018
52 8
r 100
=650 = r
5200 = 8r8 It's a 650% increase
in weight.8
R = 650%
Let R = % increase
Percent error = 12.5%
Percent error = x 100 5 40 Percent error = 12.5%
Let R = % error
Percent error = 25%
Percent error = x 100 100 400 Percent error = 25%
Let R = % error
13.49 75.99
r 100
= 17.7523... = r
1349 = 75.99r
The price decreased about 17.8%.R ≈ 17.8%
75.99 75.99Let R = % increase
NEW Review Guide (With Answers).notebook June 04, 2018
Total = 20 pens
7 20
1 40 (impossible)
1 (certain)3 + 4
3 80
= 3 20
5 20
#5 1 20
= 4 20
5 20
#6
1 19
= 4 19
5 20
#7
1 57
= 3 20
8 19
#8 3 50
= 8 20
3 20
#9 5 18
6 20
3 10
=
6 20
n 150
=
45 = n
900 = 20n20
Let n = # of times expected to land on the sun
20n = x 150 6
20
You would expect the spinner to land on the sun 45 times
n = 45
Total = 50 rolls
34 50
x 10,000 = 6800
skirtsblousesx3 4 = 12 12 outfits
coin #2coin #1x2 2 = 8 8 outcomesx
coin #32
NEW Review Guide (With Answers).notebook June 04, 2018
158 9
= 17.5
11, 12, 15, 17, 18, 19, 20, 21, 25
median = 18mode = none
meanmean = 17.5
median
range 25 - 11 = 14
range = 14
1, 2, 3, 3, 4, 4, 5, 6, 6, 7 median = 4lower extreme = 1upper extreme = 7
1st Quartile = 33rd Quartile = 6
Title
# of items
Electronics World
AIt's median time is 5 minutes faster, it also has a lower range and IQR (interquartile range)
50%75%
time is 5 minutes faster, it also has a lower range and IQR (interquartile range) so it's data are more clustered together.
A It's median
NEW Review Guide (With Answers).notebook June 04, 2018
C = πdC = π 20C = 20π
C ≈ 62.8 mm
A = πr2
A = π (10)2
A = 100π
d = 20, so r = 10
A ≈ 314.2 mm2C = 62.8318... A = 314.1592...
C = πdC = π 10C = 10π C = 10π m
C = 2πr C = 2 π 10C = 20π C = 20π in
A = πr2 A = π (6)2
A = 36πd = 12, so r = 6
A = 36π in2
6 = rThe radius is 6 meters.
C = 2πr 12π = 2 π r 2π 2π
12π = 2 π r
radius = 6 in
√√A = πr2 36π = πr2
π π
36π = πr2
36 = r2
±6 = r
The diameter is 12 inches
18 = d
C = πd18π = π d18π = πd π π
d = 18 so r = 9 A = πr2
A = π (9)2
A = 81πA = 81π cm2
NEW Review Guide (With Answers).notebook June 04, 2018
AB
A A = lwA = 9 8 A = 72
BA = 5 2A = 10
Total Area = 72 - 10Total Area = 62 yd2
A = lw
Total Area = A - B8 yd
SA = 550 m2
l w
h
V = lwhV = (15)(5)(10)V = 750 m3
SA = 2lw + 2wh + 2hl = 2(15)(5) + 2(5)(10) + 2(10)(15) = 150 + 100 + 300
= 550
SA = 2πr2 + 2πrhSA = 2π(5)2 + 2π(5)(4)SA = 50π + 40πSA = 90π SA = 90π in2 SA ≈ 282.7 in2
V = πr2hV = π(5)2 4 V = 100π
V = 100π in3
V ≈ 314.2 in3
NEW Review Guide (With Answers).notebook June 04, 2018
13
V = πr2h13
V = π(4)2 25
V = 133.3π
diameter = 8, so radius = 4
V = 133.3π ft3 V ≈ 418.9 ft3
Maxwell should find its volume because volume is the amount of space a 3dimensional figure occupies.
Area of front/backA = lw A = 3 x 2A = 6
frontside
top Area of Sides (2)A = lw A = 2 x 1A = 2
SA = 6 + 6 + 2 + 2
SA = 16 ft2
V = lwhV = (6)(2.5)(4)V = 60 in3
Volume of 1 box of crayons
240 60 = 14,400They need 14,400 cubic inches of space to store the crayons.
V = πr2h81π = π(3)2 h height = 9m81π = 9πh
81π = 9πh 9π9π
9 = h
V = lwh40 = 4 2 h 40 = 8h
885 = h
height = 5m
NEW Review Guide (With Answers).notebook June 04, 2018
50125
135
48 + 37 + 111 = 196No
10 + 70= 80
8 10 = 80
180 - 80= 100
100 3 21 + 12= 75
21 - 6= 15 7 22 - 38
= 116
3 22 - 2= 64
vertical angles
x = 10
7
- x- 1x
7
8x = x + 70
7x = 70
complementary
x = 214
3x + 12 + x - 6 = 90
- 6
4
4x + 6 = 90- 64x = 84
supplementary
x = 2210
7x - 38 + 3x - 2 = 180
+ 40
10
10x - 40 = 180+ 4010x = 220
38 + 68 + y = 180106 + y = 180
- 106 - 106y = 74
The other angle is 74
Let y = the measure of other angle
NEW Review Guide (With Answers).notebook June 04, 2018
36
2x90 + 36 + 2x = 180
126 + 2x = 180- 126 - 126
2x = 542 2x = 27
x = 27
45 + 110 + 65 + x = 360220 + x = 360
- 220 - 220x = 140
The m W is 140
Let y = m W
x + x + 5 + x + 15 + 2x = 3605x + 20 = 360
- 20 - 20
x = 68
5x = 3405 5
m A = 68
m B = 68 + 5 = 73
m C = 68 + 15 = 83
m D = 2(68) = 136
12 - 21.
12)
30
Vertical to 2 OR supp. to 4 or 1150 It is supplementary to 4 or 1
Alt. interior to 4 OR corresponding to 1 150
17 *The sum of the 3 angles of a triangle is 180
30Vertical to 5 OR alt. exterior to 1 OR
corresponding to 430
They are alternate exterior
They are correspondingThey are alternate interior
NEW Review Guide (With Answers).notebook June 04, 2018
AB BAor
AC CAorC
Bscalene
right
NEW Review Guide (With Answers).notebook June 04, 2018
AC CAor
AB BAorB
Cscaleneobtuse
6 + 8 > 914 > 8 (True) Yes
Sum: 6 + 9 = 15Difference: 9 6 = 3
The third must be greater than 3 inches, but less than 15 inches.
√
a2 + b2 = c2
162 + b2 = 302
256 + b2 = 900
b2 = 644- 256 - 256
√ b = ± 2 161 2 161 meters √√
a2 + b2 = c2
102 + 122 = c2
100 + 144 = c2
244 = c2√√ ± 2 61 = c √
2 61 feet√
50 fthouse
40 ftground
x
tree
√
a2 + b2 = c2
402 + b2 = 502
1600 + b2 = 2500
b2 = 900- 1600 - 1600
√ b = ± 30
The tree hit the house 30 feet
above the ground.
NEW Review Guide (With Answers).notebook June 04, 2018
y2 y1x2 x1
ΔyΔx
slope = =x1 y1 x2 y2
5 - 14 - -3 = 7
4
slope = 74
y2 y1x2 x1
x1 y1 x2 y2
5 - 63 - 2 = 1
-1
slope = -1
y2 y1x2 x1
slope = -2y-intercept = 7
slope = y-intercept = -5
21 slope = 5
y-intercept = 1
NEW Review Guide (With Answers).notebook June 04, 2018
xintercept (let y=0)
12 = 6x6
xint = 2
12
yintercept (let x=0)
y = 6x + 12
y = 122 = xyintercept = 12
y = 6(0) + 12
y = 6x + 120 = 6x + 12
12
6
xintercept (let y=0)
4 4x = 4
3
xintercept = 4
3
yintercept (let x=0)
y 4x = 3
y = 3yintercept = 3
y 4(0) = 3
y 4x = 30 4x = 34x = 3
y = x + 521 y = 5x 3 y = x 6
slope = -2y-intercept = 3up 2 left 1
2-1
-21
down 2 right 1
ORslope = -2y-intercept = -4
up 2 left 1
2-1
-21
down 2 right 1
OR
y = 2x + 3
y = 2x + 3 TP
Test Point (3,2)x, y
True
y ≥ -2x - 4
2 ≥ -2(3) - 41 ≥ -10
NEW Review Guide (With Answers).notebook June 04, 2018
xintercept (let y=0)
12 = 6x6
xint = 2
12
yintercept (let x=0)
y = 6x + 12
y = 122 = xyintercept = 12
y = 6(0) + 12
y = 6x + 120 = 6x + 12
12
6
xintercept (let y=0)
4 4x = 4
3
xintercept = 4
3
yintercept (let x=0)
y 4x = 3
y = 3yintercept = 3
y 4(0) = 3
y 4x = 30 4x = 34x = 3
y = x + 521 y = 5x 3 y = x 6
slope = -2y-intercept = 3up 2 left 1
2-1
-21
down 2 right 1
ORslope = -2y-intercept = -4
up 2 left 1
2-1
-21
down 2 right 1
OR
y = 2x + 3
y = 2x + 3
TP
Test Point (3,2)x, y
True
y ≥ -2x - 4
2 ≥ -2(3) - 41 ≥ -10
NEW Review Guide (With Answers).notebook June 04, 2018
y = x + 131
1
1 11
-1-1
OR
1
1
y = x 1slope = 1yintercept = 1
y = x 131y = x + 1
slope = yintercept = 1
31
1
3 13
-1-3
OR
1
3
(3, 2)
2 = 22 = 22 = (3) + 12 = 3 1Check (3, 2)
y = x 1 31y = x + 1
31
x y
y = x + 2
down 2 right 3
-23
∆y∆x
Slope23-
yintercept 2
23-
up 2 right 1
21
∆y∆x
Slope
yintercept 3
2
y = 2x 3
down 2 right 3 up 2
right 1
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Yes, every input has exactly one output
Not a function, the input -2 has 2 outputs
(2, 5)(2, -2) (4, 1)(3, 3) (6, 1){2, 3, 4, 6}{-2, 1, 3, 5}
Not a function, because the input 2 has 2 outputs.
y = 128 - 8x
If bottle is unopened, no servings have been poured, so x = 0.
y = 128 - 8(0)y = 128 - 0y = 128
NEW Review Guide (With Answers).notebook June 04, 2018
has exactly one output.
Yes, every input
I agree with the boys claim. shown in the table is NOT a function
The relation
because some inputs have 2 outputs.If we reverse the x (input) and y (output),
the relation would be a function becauseeach inputs would have exactly 1 output.
NEW Review Guide (With Answers).notebook June 04, 2018
Using the vertical line test -- Each vertical line drawn through the graph intersects at only 1 location.
A
Remember: The y-intercept is the value of y when x = 0
ΔyΔx
=slope = 44 = 1
+4 +4
Function Rule: y = x - 5
ΔyΔx
=slope = 24 = 2+2 +4
y-intercept = 1
y-intercept = -5 Function Rule y = 2x + 1
translationreflectionrotation
dilationlarger
smaller
translations, reflections and rotations are isometries
NEW Review Guide (With Answers).notebook June 04, 2018
Rule: (x,y) (x, y) A' (3, 5)
Rule: (x,y) (x, y) A' (3, 5)
Rule: (x,y) (x 2, y + 6) A' (5, 11)
Rule: (x,y) (2x, 2y) B' (4, 16)
Rule: (x,y) (y, x) R' (7, 4)
Rule: (x,y) (x, y) T' (3, 9)
A' (2, 8)T' (2, 2)
A (1, 4)T (1, 1)
M (3, 3)
H (3, 1)
M' (6, 6)
H' (6, 2)
Rule: (x,y) (2x, 2y)
H'
A'M'
T'
NEW Review Guide (With Answers).notebook June 04, 2018
A' C'
B'
B' (5, 5)C' (5, 8)
B (5, 5)C (5, 8)
A (2, 8) A' (2, 8)
Rule: (x,y) (x, y)
15
NEW Review Guide (With Answers).notebook June 04, 2018
B' (2, 5)
D' (5, 2)
B (2, 5)
D (5, 2)
A (5, 5)
C (2, 2)
A' (5, 5)
C' (2, 2)
Rule: (x,y) (x, y)
C
A B
D
C'
A'B'
D'