英语翻译The vertical line test to determine whethera curve is th

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英语翻译
The vertical line test to determine whether
a curve is the graph of a function states:If every vertical line in
the ry-plane intersects a given curve in at most one point,then
the curve is the graph of a function.Explain why this is true.
大概意思：如果任意直线最多和一直曲线有一个交点,那么这条曲线一定会对应一个方程.解释为什么以上所诉是对的.
可以用中文回答,英语解答和最快回答优先考虑采纳,过程但一定要清楚!

如图：设C（x1,y1）,D（x2,y2）设直线为y＝ax＋b,双曲线为y＝k＆＃47；x．联立消去y得：ax＾2＋bx－k＝0所以x1x2＝－k＆＃47；a．则E（0,y1）,F（x20）,所以y1＝k＆＃47；x1．直线EF的斜率为－y1＆＃47；x2＝－（　k＆＃47；x1）　＆＃47；x2＝－k＆＃47；（x1x2）＝　－k＆＃47；（－k＆＃47；a）＝az直线CD的斜率也是a．所以EF∥CD．

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