数学专业英语课后习题2.6

1.1）function，domain，range，the identity function，the absolute-value function，the real-valued function，real variable

2）cube，volume，edge-length，prime，totality

3）Hooke's law，stretch，displacement，spring，constant，proportional

4）schematic representation，plot，image，output，input

5）it is not difficult to imagine，the idea was much too limited

2.（1）常用英语字母和希腊字母来表示函数。

Letters of the English and Greek alphabets are often used to denote functions.

（2）若 f 是一个给定的函数，x 是定义域里的一个元素，那么记号f(x)用来表示由 f 确定的对应于x 的值。

If f is a given function and if x is an object of its domain, the notation f(x) is used to designate that object in the range which is associated to x by the function f.

（3）该射线将两个坐标轴的夹角分成两个相等的角。

The ray makes equal angles with the coordinates axes.

（4）可以用许多方式给出函数思想的图解说明。

The function idea may be illustrated schematically in many ways.

（5）容易证明，绝对值函数满足三角不等式。

It is easy to proof that the absolute-value function satisfies the triangle inequality.

（6）对于实数x>0，函数g(x)表示不超过x 的素数的个数。

For a given real number x>0, the function g(x) is defined by the number of primes less than or equal to x.

（7）函数是一种对应，它未必可以表示成一个简单的代数公式。

A function is a correspondence. It is not necessary to be expressed by a simple algebraic formula. （8）在函数的定义中，关于定义域和值域中的对象，没对其性质做出任何限制。

The function idea places no restriction on the nature of the objects in the domain X and in the range Y.

3.