一次函数的图像与性质(一)
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1.由函数的单调性可知,在一次函数 y= kx +b(k≠0)中,当k> 0时,y随着x的增大而增大,即单调递增;当k<0时,y随着x的增大而减小,即单调递减.另外,正比例函数y= kx(k≠0)的图像关于原点O成中心对称.
2.在解决有关一次函数的问题时,常运用分类讨论和数形结合的思想方法.对分类讨论,在解题过程中,经常分k>0或k< 0等情况进行分步解决.而对于数形结合,一方面是由数定形,确定图像的大致位置;另一方面是由形导数,即从给定的函数图像上获得信息,确定图像上点的坐标及解析式.
3.把一次函数解析式y=kx+b中的y移到右边,就得到一个关于x、y的二元一次方程kx-y+b=0,这时适合一次函数的一组x、y的值就是相应的二元一次方程的一组解.因此“一次函数”、“二元一次方程”、“直线”这三个名词有时在不至于引起混淆的情况下通用.
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