本文介绍利用直线的斜率求一类分式函数的值域.例1求函数y=(3x2-1)/(x2+2)的值域.解y可看成是点A(-2,1)与点(X,3x2)连线的斜率.设x′=x′,y′=3x2,则y′=3x′(x′≥0),故原函数的值域即为点A(-2,1)与射线y′=3x′(x′≥0)上的点(x′,y′)的连线斜率的取值范围. This article describes the use of the slope of a straight line to find a range of fractional functions. Example 1 Find the range of the function y=(3x2-1)/(x2+2). The solution y can be seen as point A (-2,1 ) The slope of the line connecting the point (X, 3x2). Let x’ = x’, y’ = 3x2, then y’ = 3x’ (x’ ≥ 0), so the range of the original function is point A (- 2,1) The value range of the line slope of the point (x’,y’) on the ray y’=3x’ (x’≥0).