쉐도잉 연습: Relations and Functions | Algebra - 영상으로 영어 말하기 배우기

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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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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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이 레슨의 어휘와 말하기 포인트

이 말하기 레슨은 영상 “Relations and Functions”을(를) 바탕으로 합니다. 가장 자주 반복되는 단어는 다음과 같습니다: value, relation, function, negative, correspond. 이 영상에는 섀도잉할 문장 124개와 단어 1357개가 있습니다. 말하는 구간의 길이는 12:25입니다. 화자는 분당 약 109단어로 천천히 말해서 소리 하나하나를 따라 하기에 여유가 있습니다. 단어의 83%가 영어에서 가장 많이 쓰이는 3,000단어에 속합니다. 나머지는 연습 전에 미리 확인해 두세요.

이 영상의 핵심 어휘

영상에 나오는 익혀 둘 만한 단어 15개를 발음, 뜻과 함께 정리했습니다.

단어	발음	뜻
relation 명사	/ɹɪˈleɪʃ(ə)n/	관계
correspond 동사	/ˌkoɹəˈspɑnd/	일치하다, 부합하다
output 명사	/ˈaʊtpʊt/	출력
vertical 형용사	/ˈvɝ.tɪ.kəl/	수직의
graph 명사	/ɡɹæf/	그래프, 도표
associate 명사	/əˈsoʊʃi.ət/	제휴자, 조합원
intersection 명사	/ˈɪntəɹˌsɛkʃən/	사거리, 네거리
diagram 명사	/ˈdaɪ.ə.ɡɹæm/	다이어그램, 도표
notify 동사	/ˈnoʊtɪfaɪ/	통치하다, 통보하다
complicated 형용사	/ˈkɑm.plɪˌkeɪ.tɪd/	복잡하다
confirm 동사	/kənˈfɝm/	확인하다
examination 명사	/ɪɡˌzæm.ɪˈneɪ.ʃən/	진찰, 검사
identical 형용사	/ɪˈdɛntɪkl̩/	동일한, 똑같은
podcast 명사	/ˈpɑdˌkæst/	팟캐스트
tutor 명사	/ˈtjuːtəː/	튜터

주의할 발음

화자는 we're, I'm, doesn't 같은 축약형과 약화된 형태를 23번 사용합니다. 들리는 대로 짧게 발음하세요.

“sh”와 “zh” 소리: relation /ɹɪˈleɪʃ(ə)n/, associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/
긴 단어 — 강세 위치에 주의: associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/

한국어 화자가 어려워하는 소리:

/f/ — ㅍ(/p/)으로 바꾸지 말고 윗니를 아랫입술에 대기: graph /ɡɹæf/, notify /ˈnoʊtɪfaɪ/, confirm /kənˈfɝm/
/z/ — ㅈ이 아니라 성대를 울리는 /s/: examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/, specialize /ˈspɛʃəˌlaɪz/

이 영상으로 연습하는 방법

먼저 말하지 않고 영상을 끝까지 듣고 모르는 단어를 적어 둡니다.
보통 속도로 한 문장씩 섀도잉하고, 화자의 리듬과 맞을 때까지 반복합니다.
자신의 목소리를 녹음해 원본과 비교하고, relation, correspond, output 같은 단어에 특히 주의합니다.

쉐도잉이란? 영어 실력을 빠르게 키우는 과학적 방법

쉐도잉(Shadowing)은 원래 전문 통역사 훈련을 위해 개발된 언어 학습 기법으로, 다언어 학자인 Dr. Alexander Arguelles에 의해 대중화된 방법입니다. 핵심 원리는 간단하지만 매우 강력합니다: 원어민의 영어를 들으면서 1~2초의 짧은 지연으로 즉시 소리 내어 따라 말하는 것——마치 '그림자(shadow)'처럼 화자를 따라가는 것입니다. 문법 공부나 수동적인 청취와 달리, 쉐도잉은 뇌와 입 근육이 동시에 실시간으로 영어를 처리하고 재현하도록 훈련합니다. 연구에 따르면 이 방법은 발음 정확도, 억양, 리듬, 연음, 청취력, 말하기 유창성을 크게 향상시킵니다. IELTS 스피킹 준비와 자연스러운 영어 소통을 원하는 분들에게 특히 효과적입니다.

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쉐도잉 연습: Relations and Functions | Algebra - 영상으로 영어 말하기 배우기

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이 레슨의 어휘와 말하기 포인트

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주의할 발음

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