y = -x^(1/3)
What type of function is this? Simplified it is y = i*cube root(x)
I'm trying to find the symmetry using the formula x = -b/2a.
the function you cite is actually $\displaystyle f(x) = -\sqrt[3]{x}$
did you mean $\displaystyle y = (-x)^{\frac{1}{3}}$ ?
if so, this is the same as $\displaystyle f(x) = -\sqrt[3]{x}$
note that $\displaystyle (-x)^{\frac{1}{3}} = (-1)^{\frac{1}{3}} \cdot x^{\frac{1}{3}} = -1 \cdot x^{\frac{1}{3}}$
no i is involved ... $\displaystyle (-1)^{\frac{1}{2}} = i$
$\displaystyle f(x) = -\sqrt[3]{x}$ is an odd function symmetric to the origin.
But how did you find the symmetry and odd/even?
I know that an even/odd power corresponds to a even/odd function, however...the power in this case is a fraction. Without graphing, how can I determined this?
BTW, what graphing tool did you use to generate that graph?
Thanks.
$\displaystyle f(x)$ is odd if $\displaystyle f(-x) = -f(x)$
$\displaystyle f(x) = \sqrt[3]{-x} = -\sqrt[3]{x}$
$\displaystyle f(-x) = \sqrt[3]{-(-x)} = \sqrt[3]{x}$
$\displaystyle f(-x) = \sqrt[3]{x}$ is the opposite of $\displaystyle f(x) = -\sqrt[3]{x}$ , therefore $\displaystyle f(x)$ is odd.
free graph program ...
Graph
The names odd & even most likely came from exponents.
But exponents really do not determine much.
For example: $\displaystyle \cos(x)$ is even and $\displaystyle \sin(x)$ is odd.
Learn the actual definitions: If $\displaystyle f(x)=f(-x)$ then $\displaystyle f$ is even.
If $\displaystyle -g(x)=g(-x)$ then $\displaystyle g$ is odd.