Arithmetic Combinations

Today we reviewed Arithmetic Combinations.
They are as follows:

(let f(x) = 3x + 2 and g(x) = x^2 - 5x)

addition - (f+g)(x) = f(x) + g(x)
     ex. (f+g)(x) = 3x + 2 + x^2 - 5x
          (f+g)(x) = x^2 - 3x + 2

subtraction - (f-g)(x) = f(x) - g(x)
    make sure to distribute the minus sign throughout the the function g(x)
    ex. (f-g)(x) = (3x + 2) - (x^2 - 5x)
         (f-g)(x) = 3x + 2 - x^2 + 5x
         (f-g)(x) = -x^2 + 8x + 2

multiplication - (fg)(x) = (f(x)) (g(x))
    ex. (fg)(x) = (3x + 2)(x^2 - 5x)
         (fg)(x) = 3x^3 - 15x^2 + 2x^2 - 10x
         (fg)(x) = 3x^3 - 13x^2 - 10x

division - (f/g)(x) = (f(x)) / (g(x))
   watch out for extraneous solutions that might not have been extraneous when the
   two functions were seperate
   ex. (f/g)(x) = (3x + 2)
                       (x^2 - 5x)
           x cannot equal 5

graphing arithmetic combinations

I'm sorry there are no graphs. For some reason I was unable to upload images. If anyone else can figure out a way to add some example graphs in a comment please do.

for addition and subtraction, add and subtract the y-coordinates
for multiplication and division, multiply and divide the y-coordinates