(例題) |
関数 |
y= |
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x |
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で、x
が2から6まで増加するときの変化の割合を求めなさい。 |
2 |
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y |
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ア… |
y= |
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x |
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イ… |
y= |
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ア |
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= |
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6 |
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= |
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イ |
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x |
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y= |
1 |
x |
2 |
の式やグラフが必要なのはここまで。 |
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0 |
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2 |
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6 |
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y |
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割合とは、「1」に対していくつ?ということだから、 |
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1 |
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4 |
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x |
× |
4 |
= |
1 |
× |
16 |
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4x=16 |
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( x の増えた量) |
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( y の増えた量) |
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x=4 |
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(答え) |
変化の割合は 4 |
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0 |
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2 |
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6 |
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別解 |
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上の解法を少し難しく言ってるのが、教科書などに載っている解法です |
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変化の割合= |
( y の増えた量) |
= |
16 |
= |
4 |
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( x の増えた量) |
4 |
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もっと簡単な別解 |
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変化の割合= |
1 |
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× |
8 |
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4 |
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2 |
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この |
1 |
は、 |
y= |
1 |
x |
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の |
1 |
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もっと簡単な別解の説明 |
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関数 |
y=ax |
2 |
で、 |
x が m から n まで増えるときの変化の割合は… |
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x = m のときの y の値は、 y = am |
2 |
(イ) |
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y |
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x = n のときの y の値は、 y = an |
2 |
(ア) |
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ア |
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変化の割合= |
( y の増えた量) |
= |
an |
2 |
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am |
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( x の増えた量) |
n - m |
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= |
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(n |
2 |
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m |
2 |
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a |
(n + m )(n - m ) |
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n - m |
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a(n + m ) |
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だから、 |
1 |
(2+6) |
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で、変化の割合が出ます |
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