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数学 高校生

なぜ、グラフの太線のところが解になるのですか?

第2章 2次関数 絶対値記号を含む関数のグラフ (1) 菜 例題 84 次の関数のグラフをかけ. (1)y=|x+2| 二方 (1)定義に戻り、絶対値記号をはずす。 「x+2 |x+2|= 冊 (1) y=|x+2| -(x+2) (x+2<0) であるから,x-2 と x<-2 に分けて考える YA x+2 (x-2) > A=(x+2) (x<-2) よって、グラフは右の図 のようになる. (2) y=x²-2x-3|xx01 (x+2=0) = (x + ²x+2) (x < -2) + ことを (x+2) ワー x+2(x-2) VIV vs+ (2) x²-2x-3=(x+1)(x-3) より, 2 =x+2のグラフとy=-(x+2) の グラフはx軸に関して対称になっている x+2≧0 だから,y=|x+2|のグラ はつねにx軸より上側 (x軸を含む) あるつき2」のグラス よって, ①,②より, グラフは右の図のようになる x-2x-3≧0 のとき、 x≦-1,3≦xS ェク =x2-2x-3<0 のとき, -1<x<3(-)+ (S-x − x) 4 3 ³ x≤-1, 3≤x 0,30 01 10 04 y=x2-2x-3|=x2-2x-3=(x-1)2-4 ……① 1<x<3のとき,ℓt=v=x s-cy=x2-2x-3|=-x2+2x+3=-(x-1)²+4 **** キー |x-2, x≦-2 のように、 x=-2はどちらの範囲に含ん m でもよい (x=-2のときの 1=ON 45+1 -2 0 x+2と-(x+2) の値が等しく なるので).普通は,解答のよ うにx≧2,x<-2 (絶対値記 号の中が0以上と負)とする. 数になる。 x R 8+vs+xb-x$+yxSfx » +^x$ — ³+²{(S+x)+x); Sty=x (1 絶対値記号のはずし方は,内が0になる前後で場合分け -140 (x+2) -3 11 12 11

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英語 高校生

英語の読解問題です。 これで合っていますか?

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