For each of the equations below, determine algebraically if the graph of that equation is symmetric with respect to x-axis, y-axis, and origin.

Question

(a)  x²+1/x³ = y²

 

(b)  lxl x³ = ³√y

Answer 1

Hi Aaron,

 

Lots of work here. if symmetric with respect to the y-axis, then f(x)=f(-x)

(-x)²+1/((-x)³) = y²  = x²-1/x³ = y² Not symmetric with respect to the y axis

If symmetric with respect to the x-axis, then f(x)=-f(x)

x²+1/x³=(-y)²  = x²+1/x³=y²     Yes, symmetric with respect to the x-axis

If symmetric with respect to the origin, then f(x)=f¹(x)    //f¹(x) being the inverse of f(x)

For this interchange x and y and see if you end up with what you started with (Hint: you shouldn't)

y²+1/x³=x²

Can you finish this?