6b - ws 6 making your own functions.sagews

%md
This is quick worksheet that hits the basics of defining your own user-built function.  Except for a few names, you can give a function just about any name you want.  Also, the function can have as many *arguments* as you want and the arguments can stand for numbers, expressions or other functions.  I will start with function that when given $m$ and $b$, will create the right side of a slope-intercept linear equation.  After that, I will create a similar function whose output will be a point-slope intercept form of a straight line using the values $m$, $x0$, $y0$.

The basic code for making your own **user-defined** functions is:

def *fn name(var1,var2,var3,...)*:

        return you want it to output

This is quick worksheet that hits the basics of defining your own user-built function. Except for a few names, you can give a function just about any name you want. Also, the function can have as many arguments as you want and the arguments can stand for numbers, expressions or other functions. I will start with function that when given $m$ and $b$, will create the right side of a slope-intercept linear equation. After that, I will create a similar function whose output will be a point-slope intercept form of a straight line using the values $m$, $x0$, $y0$.

The basic code for making your own user-defined functions is:

def fn name(var1,var2,var3,...):

    return you want it to output

m,x0,y0,b=var('m,x0,y0,b') #always safe to declare variables!!!
def slope_int_eqn(m,b):
    return m*x+b#notice the indent!

#I will test it with m=2 and b=3
slope_int_eqn(2,3)

#here's the second example
def point_slope_eqn(m,x0,y0):
    return m*(x-x0)+y0

#I will test it with m=2, x0=3, y0=4. when you execute you will notice that cocalc simplifies the result.
point_slope_eqn(2,3,4)

2*x + 3 2*x - 2