Shadowing Practice: Relations and Functions | Algebra - Learn English Speaking with Video
Bir pratik modu seçin
Her mod tam ekran bir pratik odası açar.
124 cümleler
Cümleler çok kısa veya çok uzun ise, ayarlamak için Düzenle'ye tıklayın.
1
in this video we're going to focus on relations and functions
2
so what is a relation a relation is a set of pairs of input
3
and output values here
4
we have three ordered pairs in the first relation on the
5
left the x value is the input value the y value
6
is the output value the x values is associated with the
7
domain of the relation the y values is associated with the range of the relation
8
so now let's focus on part a list the domain
9
and range of each relation so let's start with the domain
10
so what we're gonna do is we're gonna make a list of all of the x values
11
and I'm going to write it in ascendant order.
12
So first we have negative 3 and then 0 and 2.
13
Now let's write the range of that relation.
14
So we're going to focus on the y values and it's already listed in ascendant order.
15
So 1, 4, and 5.
16
Now, let's do the same thing for the other relation.
17
So, let's write out the domain.
18
So, the lowest x value is negative 2.
19
Next is 1 and then 3.
20
Now, let's write out the range of that relation.
21
The lowest y value is negative 2.
22
And then it's 3, 4, and 7.
23
So that's how you can write out the domain and range of each relation.
24
Now how can we determine if the relation is a function?
25
In order for the relation to be a function, every input value must have only one output value.
26
If an input value corresponds to two or more output values, that relation is not a function.
27
Now, let's focus on the first relation.
28
So we have the ordered pair 2 -1.
29
The input value is 2, the output value is 1.
30
And then negative 3, 4.
31
So negative 3 corresponds to 4, and then 0 corresponds to 5.
32
So for the first relation, we can see that for every input value, there's only one output value.
33
Now let's focus on the second relation.
34
So we have the ordered pair 1, 3.
35
Next is negative 2, 4.
36
And then it's 3, negative 2.
37
And then finally, negative 2, 7.
38
So for the second relation, notice that negative 2 corresponds to two different output values.
39
Now that's a problem.
40
If you put in an input value of negative 2, should the output be 4 or 7?
41
So whenever you have that situation, you know that relation is not a function.
42
The first one is a function.
43
Every input value corresponds to an output value, just one output value.
44
So a quick way to look at a relation to see if it's not going to be a function, look for repeated x values.
45
If you see two x values that are the same but correspond to two different y values, then you know the relation is not a function.
46
I want to take a minute to talk about my website video -tutor .net.
47
It's a very simple website, not too complicated,
48
but for those of you who want to be notified anytime I release specialized content in the form of a video,
49
an ebook, an article.
50
It could be a digital course or a podcast.
51
If you want to be notified, feel free to join the email list.
52
And once you confirm your email, you're going to get access to a page that has all of my playlists listed on it.
53
And this includes my final exam videos and also my test prep videos.
54
So feel free to join the email list when you get a chance.
55
And let's get back to the video.
56
Now let's move on to the next example.
57
Draw a mapping diagram of each relation shown below.
58
So let's start with the relation on the left.
59
We're going to map out the domain and the range.
60
So for the domain, we have the values negative 2, 1, and 3.
61
For the range, we have the y values, negative 6, 0, and 4.
62
Now, negative two corresponds to zero,
63
one corresponds to four, three corresponds to negative six.
64
So for every input value on the domain side, there's one corresponding output value on to range aside.
65
So this is a relation.
66
I mean this relation is a function.
67
So the answer is yes for the first relation.
68
Now let's move on to the second relation.
69
So let's create a map and diagram as well.
70
So let's start with the domain
71
The lowest x value is negative 2
72
Next we have 0
73
And then the last one is 3
74
Now looking at the y values
75
The lowest one is negative 1, and then it's going to be 1, 2, and 5.
76
So negative 2 corresponds to positive 1.
77
0 corresponds to 5.
78
3 corresponds to 2.
79
and 0 corresponds to negative 1.
80
So just by seeing the repeat x values that we see here, we could tell that this is not going to be a function.
81
The two x values have two different y values.
82
You can see 0 points to negative 1 and 5.
83
So the second relation is not a function.
84
Now for this one, what we're going to do is we're going to draw a function table of the relation.
85
And then we're going to determine if the relation is a function.
86
So in this table, we're going to list the input values next to the output values.
87
The input values represent the x values.
88
The output values represent the y values.
89
so the input values it corresponds to the domain and the output values corresponds to the range
90
so the lowest input value that we have is negative three next is one and then we have another one
91
and then after that is it's three and five
92
Now, for this function table, I'm going to write the input value twice, because that's what we have here.
93
When writing out the domain and the range, for repeat values, we would write repeat values once.
94
Now, negative 3 corresponds to 2.
95
For the table, these numbers need to match, so I'm not going to list the output values in ascending order.
96
Now, for this one, we could use either one.
97
So, I'm going to use 1, 2 for the next one, and then 1, 4.
98
Now, when x is 3, y is 7.
99
And when x is 5, y is negative 4.
100
So, that's the function table and because we have two identical x values that correspond to two different y values,
101
we know that this relation is not a function.
102
So that's it for this problem.
103
When you have a graph, the best way to determine if the graph represents a function is to use the vertical line test.
104
And that's what we're going to do in this problem.
105
So any way you draw a vertical line for the first graph, notice that the line only touches the graph at one point.
106
Therefore, the answer is yes, it represents a function.
107
For the next one on the right, if we draw a vertical line, notice at this point, or placing a line at that location,
108
we have three points of intersection between the graph and the vertical line.
109
If we can get two or more points on a vertical line, then the relation is not a function.
110
So we're going to say no. Now, if we put the vertical line here, notice that we have five points on that line.
111
So this relation is not a function.
112
For the next relation, it doesn't matter where we put the graph.
113
We will only get, I mean, it doesn't matter where we put the vertical line we're only going to get one point.
114
If we put it here, it's only going to touch the line once.
115
So we can't draw a vertical line where it touches two points.
116
Therefore, this relation represents a function.
117
For the circle, if we put the line here, we can get two points of intersection.
118
so we're going to say yes i mean no not yes
119
this is no the circle does not represent a function
120
it does not pass the vertical line test
121
it touches the line at two points in order for it
122
to pass the vertical line test the graph must touch the line only at one point
123
as we saw in these two cases.
124
So that's how you can use the vertical line test to determine if a relation represented by a graph is a function.
Uygulamayı İndir
Akıcı konuşmak için ihtiyacınız olan her şey
AI TelaffuzHer cümleyi puanla
IPA AlıştırmasıHer sesi ustalaştır
Kelime BilgisiKelime bankanızı oluşturun
Kelime OyunuOynarken öğrenin
Aynı Kanal
B11
Simplifying Fractions
American AccentHigh School StudentsUniversity Students
B1Multiplying Fractions - The Easy Way!
American AccentHigh School StudentsUniversity Students
B1Fractions
American AccentHigh School StudentsUniversity Students
B1Subtracting Fractions
American AccentHigh School StudentsUniversity Students
B1Adding Fractions With Unlike Denominators
American AccentHigh School StudentsUniversity Students
C15
First Law of Thermodynamics, Basic Introduction - Internal Energy, Heat and Work - Chemistry
American AccentIELTS PrepTOEFL PrepCambridge Exam Prep
FOR YOU
Video Öner
C11
99 cümleler
Database Normalisation: Third Normal Form
Daily ConversationUniversity Students
C11
118 cümleler
Current | Introduction to electrical engineering | Electrical engineering | Khan Academy
Daily ConversationUniversity Students
C181 cümleler
Mathematician Collapses All Functions to One Weird Formula
Daily ConversationUniversity StudentsWorking Adults
C11
177 cümleler
Pyruvate Pathways & Metabolism
Daily ConversationUniversity Students
B11
121 cümleler
What is range function and how to use it? How to trace for loop in python?
Daily ConversationUniversity Students
C11
91 cümleler
Why is water H₂O, not H₂O₂? | Lesson 7: Valency and Chemical Formulae | Science in English
Daily ConversationUniversity Students
C11
234 cümleler
Kth Smallest element in a matrix | Leetcode #378
Daily ConversationUniversity Students
C12
799 cümleler
Cell Biology | Cell Structure & Function
Daily ConversationUniversity Students
C12
63 cümleler
Unit 6: ANTHROPOLOGY/BIOLOGY: The Science of Love (Note-taking)
Daily ConversationUniversity Students
C11
95 cümleler
26 - How does harmonic phase shifting work including a detailed mathematical explanation to reduce s
Daily ConversationUniversity Students
C11
108 cümleler
Cắt bánh - bài toán gây đau đầu nhiều thế kỷ
Daily ConversationUniversity StudentsWorking Adults
C177 cümleler
1 7 What is Information
Daily ConversationUniversity Students
Bu dersin kelimeleri ve konuşma notları
Bu konuşma dersi “Relations and Functions” videosuna dayanıyor. En çok tekrarlanan kelimeler: value, relation, function, negative, correspond. Bu videoda gölgeleme çalışması için 124 cümle ve 1357 kelime var. Konuşma bölümü 12:25 sürüyor. Konuşmacı yavaş konuşuyor, dakikada yaklaşık 109 kelime; her sesi taklit etmek için zamanınız var. Kelimelerin %83’i İngilizcede en sık kullanılan 3.000 kelime arasında; geri kalanına başlamadan önce bakmakta fayda var.
Bu videodaki önemli kelimeler
Videodan öğrenmeye değer 15 kelime, telaffuzu ve anlamıyla:
| Kelime | Telaffuz | Anlam |
|---|---|---|
| relation isim | /ɹɪˈleɪʃ(ə)n/ | akraba |
| output isim | /ˈaʊtpʊt/ | çıktı |
| vertical sıfat | /ˈvɝ.tɪ.kəl/ | dikey |
| graph isim | /ɡɹæf/ | grafik |
| associate isim | /əˈsoʊʃi.ət/ | iştirakçi, ortak |
| intersection isim | /ˈɪntəɹˌsɛkʃən/ | kesişme |
| diagram isim | /ˈdaɪ.ə.ɡɹæm/ | şema |
| notify fiil | /ˈnoʊtɪfaɪ/ | bildirmek |
| complicated sıfat | /ˈkɑm.plɪˌkeɪ.tɪd/ | karışık, komplike |
| confirm fiil | /kənˈfɝm/ | onaylamak, tasdik etmek |
| examination isim | /ɪɡˌzæm.ɪˈneɪ.ʃən/ | imtihan etmek, sınav yamak |
| identical sıfat | /ɪˈdɛntɪkl̩/ | aynı, tıpa tıp aynı |
| anytime zarf | ne zaman olursa | |
| podcast isim | /ˈpɑdˌkæst/ | podcast |
| tutor isim | /ˈtjuːtəː/ | lala |
Dikkat edilecek telaffuzlar
Konuşmacı we're, I'm, doesn't gibi kısaltılmış biçimleri 23 kez kullanıyor. Bunları duyduğunuz gibi kısa söyleyin.
- “sh” ve “zh” sesleri: relation /ɹɪˈleɪʃ(ə)n/, associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/
- Uzun kelimeler — vurguyu doğru yere koyun: associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/
Türkçe konuşanların zorlandığı sesler:
- Kelime başındaki ünsüz kümesi — araya ünlü eklemeyin: graph /ɡɹæf/, tutor /ˈtjuːtəː/, playlist /ˈpleɪˌlɪst/, preposition /ˌpɹɛpəˈzɪʃən/, specialize /ˈspɛʃəˌlaɪz/
- /æ/ — “e”den daha açık: graph /ɡɹæf/, diagram /ˈdaɪ.ə.ɡɹæm/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, podcast /ˈpɑdˌkæst/
Bu videoyla nasıl çalışılır
- Videonun tamamını konuşmadan bir kez dinleyin ve bilmediğiniz kelimeleri not edin.
- Normal hızda cümle cümle tekrar edin; ritminiz konuşmacıyla aynı olana kadar her cümleyi yineleyin.
- Kendinizi kaydedin ve orijinaliyle karşılaştırın; relation, output, vertical gibi kelimelere özellikle dikkat edin.
Gölgeleme Tekniği Nedir?
Gölgeleme, başlangıçta profesyonel tercüman eğitimi için geliştirilen ve çok dilli Dr. Alexander Arguelles tarafından popüler hale getirilen, bilim destekli bir dil öğrenme tekniğidir. Yöntem basit ama güçlüdür: ana dili İngilizce olan bir sesi dinler ve hemen yüksek sesle tekrar edersiniz — konuşmacıyı 1-2 saniye gecikmeyle takip eden bir gölge gibi. Pasif dinleme veya dilbilgisi alıştırmalarının aksine, gölgeleme beyninizi ve ağız kaslarınızı gerçek konuşma kalıplarını eşzamanlı olarak işlemeye ve yeniden üretmeye zorlar. Araştırmalar, telaffuz doğruluğu, tonlama, ritim, bağlı konuşma, dinleme anlama ve konuşma akıcılığını önemli ölçüde geliştirdiğini göstermektedir — bu da onu IELTS Konuşma hazırlığı ve gerçek dünya İngilizce iletişimi için en etkili yöntemlerden biri yapar.