数学58 views·Updated Jun 25, 2026·1 page

関数とグラフの基礎理解：比例を用いた解説

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関数って聞くと難しそうだけど、実は「ある数を入れると決まった数が出てくる仕組み」のこと。自動販売機みたいに、ボタン（x）を押すと決まった商品（y）が出てくるイメージだよ。

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# 関数とグラフ

## 1. 概要

関数とは、ある数を入れると、別の数が決まるルールのこと。関数に入れる数を**変数** ($x$)、関数から出てくる数を**変数** ($y$) と呼びます。関数は、英語では function と言います。

## 2. 主な定義と概念

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関数とグラフの基本

関数は数学の中でも特に実用的な分野で、君たちの身の回りにもたくさん隠れているんだ。例えば、勉強時間と成績の関係や、気温と電気代の関係なんかも関数で表せるよ。

関数では、入力する数を変数x、出力される数を変数yと呼ぶ。これを「y = f(x)」という形で表すんだ。fは「function（関数）」の頭文字だよ。

値域は関数から出てくる数の範囲のことで、グラフは関数の関係を座標平面に描いたもの。グラフを見れば関数の性質が一目でわかるから、とても便利なツールなんだ。

💡 ポイント: 関数は「入力→処理→出力」の流れ。一つの入力に対して出力は必ず一つだけ決まる！

代表的な関数には一次関数（y = ax + b）、二次関数（y = ax² + bx + c）、三角関数（sin、cos、tan）がある。それぞれ異なる形のグラフを描くから、見分けられるようになろう。

一次関数の傾き（a）は直線の急さを、切片（b）はy軸との交点を表している。二次関数には頂点や軸といった特徴的な要素があるよ。

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