Answer
The graph passes through the origin.
The graph is symmetric with respect to the origin.
Work Step by Step
We are given the function:
$y=x^5$
Graph the function.
The graph passes through the origin.
The graph is symmetric with respect to the origin.
Comparison of the given graphs:
- all graphs pass through the origin
- the graphs of even power ($y=x^2,y=x^4,y=x^6$) are symmetric with respect to the $y$-axis, while the graphs of odd power ($y=x,y=x^3,y=x^5$) are symmetric with respect to the origin.
- as the power increases, the graphs become steeper
