Практика Shadowing: Relations and Functions | Algebra - Изучайте разговорный английский по видео

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in this video we're going to focus on relations and functions

so what is a relation a relation is a set of pairs of input

and output values here

we have three ordered pairs in the first relation on the

left the x value is the input value the y value

is the output value the x values is associated with the

domain of the relation the y values is associated with the range of the relation

so now let's focus on part a list the domain

and range of each relation so let's start with the domain

so what we're gonna do is we're gonna make a list of all of the x values

and I'm going to write it in ascendant order.

So first we have negative 3 and then 0 and 2.

Now let's write the range of that relation.

So we're going to focus on the y values and it's already listed in ascendant order.

So 1, 4, and 5.

Now, let's do the same thing for the other relation.

So, let's write out the domain.

So, the lowest x value is negative 2.

Next is 1 and then 3.

Now, let's write out the range of that relation.

The lowest y value is negative 2.

And then it's 3, 4, and 7.

So that's how you can write out the domain and range of each relation.

Now how can we determine if the relation is a function?

In order for the relation to be a function, every input value must have only one output value.

If an input value corresponds to two or more output values, that relation is not a function.

Now, let's focus on the first relation.

So we have the ordered pair 2 -1.

The input value is 2, the output value is 1.

And then negative 3, 4.

So negative 3 corresponds to 4, and then 0 corresponds to 5.

So for the first relation, we can see that for every input value, there's only one output value.

Now let's focus on the second relation.

So we have the ordered pair 1, 3.

Next is negative 2, 4.

And then it's 3, negative 2.

And then finally, negative 2, 7.

So for the second relation, notice that negative 2 corresponds to two different output values.

Now that's a problem.

If you put in an input value of negative 2, should the output be 4 or 7?

So whenever you have that situation, you know that relation is not a function.

The first one is a function.

Every input value corresponds to an output value, just one output value.

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.

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.

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If you want to be notified, feel free to join the email list.

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So feel free to join the email list when you get a chance.

And let's get back to the video.

Now let's move on to the next example.

Draw a mapping diagram of each relation shown below.

So let's start with the relation on the left.

We're going to map out the domain and the range.

So for the domain, we have the values negative 2, 1, and 3.

For the range, we have the y values, negative 6, 0, and 4.

Now, negative two corresponds to zero,

one corresponds to four, three corresponds to negative six.

So for every input value on the domain side, there's one corresponding output value on to range aside.

So this is a relation.

I mean this relation is a function.

So the answer is yes for the first relation.

Now let's move on to the second relation.

So let's create a map and diagram as well.

So let's start with the domain

The lowest x value is negative 2

Next we have 0

And then the last one is 3

Now looking at the y values

The lowest one is negative 1, and then it's going to be 1, 2, and 5.

So negative 2 corresponds to positive 1.

0 corresponds to 5.

3 corresponds to 2.

and 0 corresponds to negative 1.

So just by seeing the repeat x values that we see here, we could tell that this is not going to be a function.

The two x values have two different y values.

You can see 0 points to negative 1 and 5.

So the second relation is not a function.

Now for this one, what we're going to do is we're going to draw a function table of the relation.

And then we're going to determine if the relation is a function.

So in this table, we're going to list the input values next to the output values.

The input values represent the x values.

The output values represent the y values.

so the input values it corresponds to the domain and the output values corresponds to the range

so the lowest input value that we have is negative three next is one and then we have another one

and then after that is it's three and five

Now, for this function table, I'm going to write the input value twice, because that's what we have here.

When writing out the domain and the range, for repeat values, we would write repeat values once.

Now, negative 3 corresponds to 2.

For the table, these numbers need to match, so I'm not going to list the output values in ascending order.

Now, for this one, we could use either one.

So, I'm going to use 1, 2 for the next one, and then 1, 4.

Now, when x is 3, y is 7.

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.

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Лексика и советы по произношению к этому уроку

Этот урок разговорной практики построен на видео «Relations and Functions». Чаще всего повторяются слова: value, relation, function, negative, correspond. В этом видео 124 предложений и 1357 слов для шедоуинга. Речь длится 12:25. Говорящий говорит медленно, около 109 слов в минуту, поэтому есть время повторить каждый звук. 83% слов входят в 3000 самых частых слов английского языка; остальные стоит разобрать перед занятием.

Ключевая лексика этого видео

15 слов из видео, которые стоит выучить, с произношением и значением:

Слово	Произношение	Значение
relation существительное	/ɹɪˈleɪʃ(ə)n/	отноше́ние, зави́симость
correspond глагол	/ˌkoɹəˈspɑnd/	соотве́тствовать, согласо́вываться
output существительное	/ˈaʊtpʊt/	произво́дство, проду́кция
input существительное	/ˈɪnpʊt/	вклад
domain существительное	/ˌdəʊˈmeɪ̯n/	владе́ние
vertical прилагательное	/ˈvɝ.tɪ.kəl/	вертика́льный, отве́сный
graph существительное	/ɡɹæf/	гра́фик, диагра́мма
associate существительное	/əˈsoʊʃi.ət/	партнёр, партнёрша
intersection существительное	/ˈɪntəɹˌsɛkʃən/	перекрёсток
diagram существительное	/ˈdaɪ.ə.ɡɹæm/	план, диагра́мма
notify глагол	/ˈnoʊtɪfaɪ/	уведомля́ть, уве́домить
complicated прилагательное	/ˈkɑm.plɪˌkeɪ.tɪd/	сло́жный, запу́танный
confirm глагол	/kənˈfɝm/	укрепля́ть, укрепи́ть
examination существительное	/ɪɡˌzæm.ɪˈneɪ.ʃən/	прове́рка, иссле́дование
identical прилагательное	/ɪˈdɛntɪkl̩/	иденти́чный, одина́ковый

Фразовые глаголы, которые вы услышите

Слово	Значение
write out глагол	писа́ть по́лностью

Произношение, на которое стоит обратить внимание

Говорящий использует 23 сокращённых и редуцированных форм, например we're, I'm, doesn't. Произносите их коротко, так, как слышите.

Звуки «sh» и «zh»: relation /ɹɪˈleɪʃ(ə)n/, associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/
Длинные слова — следите за ударением: associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/

Звуки, трудные для русскоязычных:

Звонкие согласные в конце слова — не оглушайте их: correspond /ˌkoɹəˈspɑnd/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, ascend /əˈsɛnd/, specialize /ˈspɛʃəˌlaɪz/

Как заниматься с этим видео

Прослушайте всё видео один раз молча и выпишите незнакомые слова.
Повторяйте предложение за предложением на обычной скорости, пока ваш ритм не совпадёт с ритмом говорящего.
Запишите себя и сравните с оригиналом, обращая внимание на такие слова, как relation, correspond, output.

Что такое техника Shadowing?

Shadowing — это научно обоснованная техника изучения языка, изначально разработанная для подготовки профессиональных переводчиков и популяризированная полиглотом доктором Александром Аргуэльесом. Метод прост, но эффективен: вы слушаете аудио на английском от носителей языка и немедленно повторяете вслух — как тень, следующая за говорящим с задержкой в 1–2 секунды. В отличие от пассивного прослушивания или грамматических упражнений, Shadowing заставляет мозг и мышцы рта одновременно обрабатывать и воспроизводить реальные речевые паттерны. Исследования показывают, что это значительно улучшает точность произношения, интонацию, ритм, связную речь, понимание на слух и беглость речи — что делает его одним из самых эффективных методов для подготовки к IELTS Speaking и реального общения на английском.

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Практика Shadowing: Relations and Functions | Algebra - Изучайте разговорный английский по видео

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