calculus!!!!!!!!!!

dividing polynomials

100

(x^2 + 4x)/5x

(x+4)/5

200

((x^2 - 9)/2x) / ((x+3)/5)

5(x-3) / 2x

300

((x^2+5x+6)/2x^2) / ((x^2)-9)/4x

((2(x+2)/x(x-3))

400

x^2+3x+2/2x^2+4x / x^2-1/x^2+2x+1

(x+1)^2 / 2x(x-1)

500

(x^4-16/x^2-4) / (x^2-2x/x)

x^2+4 / x-2

factoring

100

x^2 + 5x + 6

(x+2) (x+3)

200

3x^2 - 8x -3

(3x+1)(x-3)

300

4x^2 - 12x +9

(2x-3)^2

*a^2 - 2ab + b^2 = (a-b)^2

4x^2 = (2x)^2

9 = 3^2

400

x^3 + 3x^2 + 2x + 6

(x^2+2) / (x+3)

500

2x^3 + 4x^2 + 3x + 6

(x+2)(2x^2+3)

function? or not?

100

y=2x+5

yes

200

x^2+y^2=25

no (circle fails vertical line test; a single x gives 2 different y values)

300

y = |x|

yes, for every x, only 1 output

400

y^2 = x

no, sideways parabola fails vertical line test

500

{(1,2),(2,3),(3,4),(4,5)} 

&

{(1,2),(1,3),(2,4),(3,5)}

yes, each input (x) has exactly 1 output (y)

no, the x value of 1 maps to 2 outputs (2&3)

*think of it as there cannot be any "<" signs from the x values

mixed

100

(2x-3)(x^2+4)

2x^3-3x^2+8x-12

200

9x^2-16

(3x-4)(3x+4)

300

x^1/7 (imagine it in root form) = y + 9

function or not?

yes

*x^1/7 means the 7th root of x. 7 is odd, and odd roots are-single valued, thus it is a function.

400

x^3-8/x^2+2x / x^2-4/x

x^2+2x+4 / (x+2)^2

500

x^2+3x+2/2x^2+4x / x^2-1/x^2+2x+1

(x+1)^2 / 2x(x-1)