在高中数学教学中 ,对函数的图象及性质的学习占有相当的比例 ,特别是对一些典型函数的研究可以培养思维能力 ,提高思维品质 .本文简要介绍函数 f(x) =ax +bx(a0 ,b0 )的性质 (单调性、值域和图象 )及应用 .一、函数 f(x)的性质1 单调性函数 f(x) =ax+bx(a0 ,b0 )的定义域 In high school mathematics teaching, there is a considerable proportion of the study of the images and properties of the function, especially the study of some typical functions can cultivate the thinking ability and improve the quality of thinking. This paper briefly introduces the function f(x) = ax + bx ( A0, b0) properties (monotonicity, range, and image) and applications. I. Properties of function f(x) 1 Domain of monotonicity function f(x) = ax + bx (a0, b0)