シャドーイング練習: Relations and Functions | Algebra - 動画で英語スピーキングを学ぶ

練習モードを選ぶ

各モードは全画面の練習ルームで開きます。

124 文

文が短すぎたり長すぎる場合は、Editをタップして調整してください。

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.

I want to take a minute to talk about my website video -tutor .net.

It's a very simple website, not too complicated,

but for those of you who want to be notified anytime I release specialized content in the form of a video,

an ebook, an article.

It could be a digital course or a podcast.

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

And once you confirm your email, you're going to get access to a page that has all of my playlists listed on it.

And this includes my final exam videos and also my test prep videos.

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.

アプリをダウンロード

流暢に話すために必要なすべて

AI発音採点文ごとに採点

IPA練習すべての音をマスター

単語学習自分の単語帳を作る

単語ゲーム遊びながら覚える

QRをスキャン

Download on theApp Store Get it onGoogle Play

同じチャンネル

Multiplying Fractions - The Easy Way!

High School StudentsUniversity Students

Adding Fractions With Unlike Denominators

High School StudentsUniversity Students

First Law of Thermodynamics, Basic Introduction - Internal Energy, Heat and Work - Chemistry

IELTS PrepTOEFL PrepCambridge Exam Prep

FOR YOU

このレッスンの語彙とスピーキングのポイント

このスピーキングレッスンは、動画「Relations and Functions」を教材にしています。繰り返し出てくる語は次のとおりです：value, relation, function, negative, correspond。この動画には、シャドーイング用の文が124文、単語が1357語あります。音声の長さは12:25です。話す速さはゆっくりで、1分あたり約109語です。一つ一つの音をまねる余裕があります。単語の83%は英語の頻出3,000語に含まれます。残りは練習の前に確認しておきましょう。

この動画の重要語彙

動画に出てくる覚えておきたい単語15語を、発音と意味つきで紹介します。

単語	発音	意味
relation 名詞	/ɹɪˈleɪʃ(ə)n/	関係, 関連
correspond 動詞	/ˌkoɹəˈspɑnd/	文通する
output 名詞	/ˈaʊtpʊt/	出力
vertical 形容詞	/ˈvɝ.tɪ.kəl/	垂直の, 縦の
graph 名詞	/ɡɹæf/	グラフ, 図表
associate 名詞	/əˈsoʊʃi.ət/	提携者
intersection 名詞	/ˈɪntəɹˌsɛkʃən/	交差点
diagram 名詞	/ˈdaɪ.ə.ɡɹæm/	ダイヤグラム, 図表
notify 動詞	/ˈnoʊtɪfaɪ/	通告する, 通知する
complicated 形容詞	/ˈkɑm.plɪˌkeɪ.tɪd/	複雑な
confirm 動詞	/kənˈfɝm/	確認する
examination 名詞	/ɪɡˌzæm.ɪˈneɪ.ʃən/	診察, 検査
identical 形容詞	/ɪˈdɛntɪkl̩/	同一の, そっくりの
anytime 副詞		いつでも
podcast 名詞	/ˈpɑdˌkæst/	ポッドキャスト

注意したい発音

話し手はwe're, I'm, doesn'tなど、短縮形や弱形を23回使っています。聞こえたとおりの短い形で発音しましょう。

「sh」と「zh」の音: relation /ɹɪˈleɪʃ(ə)n/, associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/
長い単語（アクセントの位置に注意）: associate /əˈsoʊʃi.ət/, intersection /ˈɪntəɹˌsɛkʃən/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, examination /ɪɡˌzæm.ɪˈneɪ.ʃən/, preposition /ˌpɹɛpəˈzɪʃən/

日本語話者が苦手な音：

/f/ — 「フ」ではなく、上の歯と下唇で出す: graph /ɡɹæf/, notify /ˈnoʊtɪfaɪ/, confirm /kənˈfɝm/
子音の連続 — 間に母音を入れない: correspond /ˌkoɹəˈspɑnd/, graph /ɡɹæf/, complicated /ˈkɑm.plɪˌkeɪ.tɪd/, podcast /ˈpɑdˌkæst/, tutor /ˈtjuːtəː/

この動画での練習方法

まず声を出さずに動画を最後まで聞き、知らない単語をメモします。
通常の速度で一文ずつシャドーイングし、話し手のリズムに合うまで繰り返します。
自分の声を録音して元の音声と比べます。relation, correspond, outputなどの単語に特に注意しましょう。

シャドーイングとは？英語上達に効果的な理由

シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。

シャドーイングのやり方: ステップ別の完全ガイドを読む →

シャドーイング練習: Relations and Functions | Algebra - 動画で英語スピーキングを学ぶ

練習モードを選ぶ

アプリをダウンロード

同じチャンネル

Simplifying Fractions

Multiplying Fractions - The Easy Way!

Fractions

Subtracting Fractions

Adding Fractions With Unlike Denominators

First Law of Thermodynamics, Basic Introduction - Internal Energy, Heat and Work - Chemistry

おすすめ動画

Database Normalisation: Third Normal Form

Current | Introduction to electrical engineering | Electrical engineering | Khan Academy

Mathematician Collapses All Functions to One Weird Formula

Pyruvate Pathways & Metabolism

What is range function and how to use it? How to trace for loop in python?

Kth Smallest element in a matrix | Leetcode #378

Cell Biology | Cell Structure & Function

Unit 6: ANTHROPOLOGY/BIOLOGY: The Science of Love (Note-taking)

26 - How does harmonic phase shifting work including a detailed mathematical explanation to reduce s

Cắt bánh - bài toán gây đau đầu nhiều thế kỷ

1 7 What is Information

► 2. СВОЙСТВА МАССИВОВ. Функции автозаполнения | Курс по Numpy.

このレッスンの語彙とスピーキングのポイント

この動画の重要語彙

注意したい発音

この動画での練習方法

シャドーイングとは？英語上達に効果的な理由