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英語 中学生

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[B] The Threat of Tourism As air travel gets cheaper, more and more people are visiting famous sites around the world. Although this increase in tourism brings economic benefits to the areas around these sites, tourists also cause unexpected problems. In particular, some famous works of art are being affected. This is because people's breath increases carbon dioxide and humidity levels. Gradually, these levels damage, old paintings and other works of art. One famous site facing this problem is the Sistine Chapel in the Vatican in Rome. The 500-year-old paintings, especially the famous ceiling by Michelangelo, are so popular that as many as 2,000 people may be viewing them at a time. In 1994, after noticing that the visitors' breath was damaging the paintings, the Vatican purchased an expensive air-conditioning system to protect them. However, the crowds continued to increase, so in 2014, the Vatican decided to limit the number of visitors to about 6 million a year. Another site that faces a similar problem is the Mogao Caves in Dunhuang, China. These caves are full of beautiful Buddhist paintings and sculptures that attract thousands of visitors every year. Many of the artworks are very old and, as with the Sistine Chapel, the carbon dioxide in the breath of visitors is gradually damaging them. Originally, 40 of the 400 caves were open to visitors, but this number was reduced by half in 2014. In addition, the number of visitors allowed into the caves has been greatly reduced. A different solution is being tried in the Ajanta Caves in Maharashtra, India. The caves also have many ancient Buddhist paintings in them, and these too are being damaged. In order to protect the paintings, visitors are quickly rushed through the caves. However, many visitors complained about the short time, saying they could not look at the paintings properly, so the local government built a visitors' center with exact copies of the caves. Visitors are allowed to study these copies for as long as they like. The local government hopes this will provide a good balance between protecting the paintings and giving tourists a good experience. (30) As the number of tourists increases, 1 unexpected economic problems occur among people living around famous sites. 2 the carbon dioxide and humidity in their breath harm the things they go to see. 3 air pollution caused by the carbon dioxide from airplanes increases. 4 people have trouble breathing because of the high levels of humidity. (31) In 1994, the Vatican 1 allowed only 2,000 tourists to look at its paintings by Michelangelo. 2 invited 6 million visitors to see its 500-year-old wall paintings on one day. 3 installed an air-conditioning system in order to make visitors more comfortable. 4 tried to reduce damage to its paintings by buying an air- conditioning system. (32) What is one thing that has been done to protect the Buddhist artworks in Dunhuang? 1 More of the Mogao Caves have been closed to visitors. 2016年度第2回 新試験 2 Visitors are being asked to avoid breathing too close to the paintings. 3 Some of the visitors are being taught new ways to preserve paintings. 4 The number of visitors has been reduced from 400 to 40 a day. (33) Why were some visitors to the Ajanta Caves unhappy? 1 The majority of the paintings have turned out to be copies. 2 There were not as many Buddhist paintings as they had expected to see. 3 They did not have enough time to look at the paintings inside the caves. 4 The long lines at the visitors' center have prevented them from seeing the paintings. 29

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数学 高校生

青チャート71です (1)のグラフをどう読み取ったら(2)のグラフになるのかわかりません

000 利用する 。 す。 ° 重要 例題 71 定義域によって式が異なる関数 関数f(x) (0≦x≦4) を右のように定義すると 次の関数のグラフをかけ。 (1) y=f(x) (2) y=f(f(x)) 00000 2x (0≦x<2) f(x)=| 8-2x (2≦x≦4) 指針 定義域によって式が変わる関数では,変わる境目のx,yの値に着目。 (2) f(f(x)) f(x)のxにf(x) を代入した式で、 f(x) <2のとき2f(x), 2f(x) 4のとき 8-2f(x) (1) のグラフにおいて, f(x) < 2 となるxの範囲と, を見極めて場合分けをする。 f(x)となるxの範囲 123 3章 ⑧関数とグラフ 1 2.3 0 1 2 3 (1) グラフは図 (1) のようになる。 2f(x) (0≦f(x)<2) 解答 (2) f(f(x))= 18-2f(x) (2≦f(x)≦4) よって, (1) のグラフから 0≦x<1のとき f(f(x))=2f(x)=2.2x=4x f(f(x))=8-2f(x)=8-2(8-2x) =4x-8 1≦x<2のとき f(f(x)) =8-2f(x)=8-2.2x =8-4x 1 2≦x≦3のとき O 3<x≦4のとき 2-12 よって, グラフは図 (2) のようになる。 (1) (2) -2 YA yA 4--- f(f(x))=2f(x)=2(8-2x) =16-4x AM. 1 2 3 0 1 2 3 4 + 変域ごとにグラフをかく。 (1)のグラフから,f(x) の変域は 0≦x<1のとき 0≤f(x)<2 1≦x≦3のとき 2≤f(x)≤4 3<x≦4のとき 0≤f(x)<2 また, 1≦x≦3のとき, f(x) の式は 1≦x<2なら f(x)=2x 2≤x≤375 f(x) =8-2x のように, 2を境にして 式が異なるため, (2) は左 の解答のような合計4通 りの場合分けが必要に なってくる。 nを数 n+1が成 であり, (3) 8から2倍を 引く 4-- 【参考 (2) のグラフは、式の意味を考える方法でかくこともできる。 [1] f(x) が2未満なら2倍する。 [2]f(x) 2以上4以下なら, 8から2倍を引く。 [右の図で, 黒の太線・細線部分が y=f(x), 赤の実線部分が y=f(f(x)) のグラフである。] なお,f(f(x)) f(x) f(x) の 合成関数といい, (fof) (x) と書く (詳しくは数学Ⅲで学ぶ)。 2 練習 関数f(x) (0≦x<1) を右のように定義するとき, ③ 71 次の関数のグラフをかけ。 (1) y=f(x) (2)y=f(f(x)) 0 4 x 2倍する (2x (0≦x<1/12) f(x)= 2x-1 (12/2≦x<1)

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