24.某班“數(shù)學(xué)興趣小組”對(duì)函數(shù)y=x
2-2|x|-3的圖象和性質(zhì)進(jìn)行了探究,探究過(guò)程如下,請(qǐng)補(bǔ)充完整.
(1)自變量x的取值范圍是全體實(shí)數(shù),x與y的幾組對(duì)應(yīng)值如下:
x |
… |
-3 |
- |
-2 |
-1 |
0 |
1 |
2 |
|
3 |
… |
y |
… |
0 |
- |
m |
-4 |
-3 |
-4 |
-3 |
- |
0 |
… |
其中,m=
;
(2)根據(jù)表中數(shù)據(jù),在如圖所示的平面直角坐標(biāo)系中描點(diǎn),并畫出了函數(shù)圖象的一部分,請(qǐng)畫出該函數(shù)圖象的另一部分;
(3)觀察函數(shù)圖象,寫出兩條函數(shù)圖象的性質(zhì)
;
(4)進(jìn)一步探究函數(shù)圖象發(fā)現(xiàn):
①函數(shù)圖象與x軸有
個(gè)交點(diǎn),所以對(duì)應(yīng)的方程x
2-2|x|-3=0有
個(gè)實(shí)數(shù)根;
②函數(shù)圖象與直線y=-3軸有
個(gè)交點(diǎn),所以對(duì)應(yīng)的方程x
2-2|x|-3=-3有
個(gè)實(shí)數(shù)根;
③關(guān)于x的方程x
2-2|x|-3=a有4個(gè)實(shí)數(shù)根時(shí),a的取值范圍是
;
④不等式x
2-2|x|>3的解集是
.