calculus_one What is a function?

2017_11_21 7:45

I sort understand what numbers do more than what they are in some metaphysical sense. The same is true about functions.

A function assigns to each number in its domain another number.

f(2) is 4 or f(3) is 9 Or f(4) is 16 of f(5) is 25.And I'm telling you what number it assigns to each number.I'm not going to just list off every single assignment that f makes.So instead, one way to talk about these assignments is to use a rule, like f(x) = x^2. And this single rule explains how all of these assignments are made,

Unless, I say otherwise, the domain consists of all numbers for which the
rule makes sense, right? f(x) = 1/x, I'll summarize that by saying that the domain of f is all real numbers except zero.

piecewise notation(分段符号)

C(x) is the number of even digits in the number x, when x is a whole number.It is zero if x isn't a whole number(整数), so otherwise.

And I'll say that the value of B(x) is some rearrangement of the digits of x. A function is suppose to take its input and produce unambiguously a single output value. But this so-called function takes this single input value and purportedly produces all these possible outputs. This thing here is not a function

programming

求一个多项式函数(3x^2+2*x+1)在某点(10)的函数值
1.python version

f = lambda x:3*x**2 + 2*x +1
f(10)

2.ruby version

f = lambda{|x| 3*x**2 + 2*x +1}
f.call(10)