题干

已知函数f(x)是定义在R上的偶函数,当x≥0时,f(x)=x2﹣2x﹣1.

(1)求f(x)的函数解析式,并用分段函数的形式给出;

(2)作出函数f(x)的简图;

(3)写出函数f(x)的单调区间及最值.

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答案(点此获取答案解析)

【解答】(1)当x<0时,﹣x>0,则f(﹣x)=(﹣x)2﹣2(﹣x)﹣1=x2+2x﹣1,∵f(x)是偶函数,∴f(x)=f(﹣x)=x2+2x﹣1,∴f(x)=x2

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    Plastic is easy, convenient, cheap and long-lasting, but it does great harm to the environment.

    Since plastic entered mass production, 8 billion tons have been produced – and we aren't very good at recycling. By 2015, 6,945 tons of plastic waste had formed, with around 9 percent of it getting recycled. About 79 percent of it ends up in landfills or around the environment, including the ocean. We may end up drowning in plastic before long.

    Chemists at Colorado State University have found a polymer(聚酯)that has many of the qualities of plastics – it's light, strong, durable and heat-resistant – but that can be changed back to its original small-molecule(分子)state for complete recycling. Even after being recycled, the polymer can be turned back into its plastic-like state, and this can be done quickly and cheaply.

    This new polymer has all the good qualities of plastics, yet it is relatively easy to make and to recycle. Making it requires room temperature conditions, a short reaction time to bond the monomer(单体)into polymers and only a small amount of the catalyst(催化剂)remains in the end product. It has a high molecular weight, stands up to heat and generally behaves like plastic. Recycling it requires similarly little effort. Mild lab conditions are required and so is a catalyst. Once applied, the polymers are once again monomers in a matter of minutes and can be used to create another product.

    But don't get too excited about this just yet. Scientists stressed that the polymer isn't ready for mass products just yet. There's still plenty of development to do, including making it more economical to produce and recycle.