Question

how do I graph this function?

x^2-xy+2x-1=0

Answer 1

x ^ 2 - x y + 2 x - 1 = 0 Add xy to both sides

x ^ 2 - x y + 2 x - 1 + x y = 0 + x y

x ^ 2 + 2 x - 1 = x y

Roots :

When y = 0 then :

x ^ 2 + 2 x - 1 = x * 0

x ^ 2 + 2 x - 1 = 0 Add 2 to both sides

x ^ 2 + 2 x - 1 + 2 = 0 + 2

x ^ 2 + 2 x + 1 = 2

________________________________________

Remark :

x ^ 2 + 2 x + 1 = ( x + 1 ) ^ 2

________________________________________

( x + 1 ) ^ 2 = 2 Take the square root of both sides

x + 1 = + OR - sqrt ( 2 ) Subtract 1 to both sides

x + 1 - 1 = + OR - sqrt ( 2 ) - 1

x = + OR - sqrt ( 2 ) - 1


x1 = sqrt ( 2 ) - 1 = approx 0.41

x2 = - sqrt ( 2 ) - 1 = approx. - 2.41



Revrite x ^ 2 + 2 x - 1 = x y

Divide both sides by x

x ^ 2 / x + 2 x / x - 1 / x = x y / x

x + 2 - 1 / x = y

y = x - 1 / x + 2


for x = 0

x - 1 / x + 2 -> + OR - infinity


Go on wolfram alpha dot com

When page be open in rectangle type :

plot x ^ 2 - x y + 2 x - 1 = 0

and click option =

You will see graph