题干

阅读下面材料:

如图1,在平面直角坐标系xOy中,直线y1=ax+b与双曲线y2=

k
x
交于A(1,3)和B(﹣3,﹣1)两点.

观察图象可知:

①当x=﹣3或1时,y1=y2

②当﹣3<x<0或x>1时,y1>y2,即通过观察函数的图象,可以得到不等式ax+b>

k
x
的解集.

有这样一个问题:求不等式x3+4x2﹣x﹣4>0的解集.

某同学根据学习以上知识的经验,对求不等式x3+4x2﹣x﹣4>0的解集进行了探究.

下面是他的探究过程,请将(2)、(3)、(4)补充完整:

⑴将不等式按条件进行转化:

当x=0时,原不等式不成立;

当x>0时,原不等式可以转化为x2+4x﹣1>

4
x

当x<0时,原不等式可以转化为x2+4x﹣1<

4
x

⑵构造函数,画出图象

设y3=x2+4x﹣1,y4=

4
x
,在同一坐标系中分别画出这两个函数的图象.

双曲线y4=

4
x
如图2所示,请在此坐标系中画出抛物线y3=x2+4x﹣1 ____;(不用列表)

⑶确定两个函数图象公共点的横坐标

观察所画两个函数的图象,猜想并通过代入函数解析式验证可知:满足y3=y4的所有x的值为____

⑷借助图象,写出解集

结合(1)的讨论结果,观察两个函数的图象可知:不等式x3+4x2﹣x﹣4>0的解集为____

上一题 下一题 0.0难度 选择题 更新时间:2019-11-11 09:35:40

答案(点此获取答案解析)

,±1和﹣4,x>1或﹣4<x<﹣1

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菜豆种子和玉米种子结构的相同点是都有种皮和____ ,结构上的主要区别是:与玉米种子相比,菜豆种子没有____ 。

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阅读理解

    A popular saying goes, “Sticks and stones may break my bones, but words will never hurt me.” However, that's not really true. Words have the power to build us up or tear us down. It doesn't matter if the words come from someone else or ourselves — the positive and negative effects are just as lasting.

    We all talk to ourselves sometimes. We're usually too embarrassed to admit it, though. In fact, we really shouldn't be because more and more experts believe talking to ourselves out loud is a healthy habit.

    This “self-talk” helps us motivate ourselves, remember things, solve problems, and calm ourselves down. Be aware, though, that as much as 77% of self-talk tends to be negative. So in order to stay positive, we should only speak words of encouragement to ourselves. We should also be quick to give ourselves a pat on the back. The next time you finish a project, do well in a test, or finally clean your room, join me in saying “Good job!”

    Often, words come out of our mouths without us thinking about the effect they will have. But we should be aware that our words cause certain responses in others. For example, when returning an item to a store, we might use warm, friendly language during the exchange. And the clerk will probably respond in a similar manner. Or harsh (刻薄的) and critical language will most likely cause the clerk to be defensive.

    Words possess power because of their lasting effects. Many of us regret something we once said. And we remember unkind words said to us! Before speaking, we should always ask ourselves: Is it true? Is it loving? Is it needed? If what we want to say doesn't pass this test, then it's better left unsaid.

    Words possess power: both positive and negative. Those around us receive encouragement when we speak positively. We can offer hope, build self-esteem (自尊) and motivate others to do their best. Negative words destroy all those things. Will we use our words to hurt or to heal? The choice is ours.

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