2b - ws 2b defining functions and equations .sagews

We usually think of a function as something that takes a numerical input and yields a numerical output. But that idea just scratches of the surface. First, inputs and outputs don't have to be numbers, they can be any computer entity whatsoever. Secondly, a function doesn't have to operate on a single input, but can be defined to deal with multiple inputs. In this worksheet we look at just a few ideas that will expand your horizon as far as functions go.

We look at a few different instances of functions that show up. The first is what is called a symbolic function--one in which we give it a name but haven't defined what it does. I will create the function called fnc whose input variable is just x.

fcn=function('fcn')(x) #please notice the syntax, name is wrapped in ' marks and the variable(s) afterwards in ()
show(fcn)
#going to add 5 to this function
show(fcn+5)

Now I will work with some more familiar functions. Here comes several simple examples.

1. The straight line $f(x)=2x+3$

2. The quadratic function, $quad(x)=4x^2-5x-7$

3. Now a function of 2 variables that will compute the area of a triangle. $area(b,h)=bh/2$

f(x)=2*x+3
f(4)#evaluating at x=4
quad(x)=4*x^2-5*x-7
quad(0)
b,h=var('b,h')#don't forget to declare new variables!!!!!!!!!
area(b,h)=b*h/2
area(5,10)

Precalc tells us we can add functions together. sage knows this. . .

f(x)=2*x+3
quad(x)=4*x^2-5*x-7
b,h=var('b,h')#don't forget to declare new variables!!!!!!!!!
area(b,h)=b*h/2
#here comes some examples
3*f(x)
quad(x)-f(x)
(f(x))^2
area(b,h)+quad(x)