# How do you graph y=x^5?

Jul 27, 2018

below

#### Explanation:

The graph $y = {x}^{5}$ is an odd function and has an intercept at $\left(0 , 0\right)$. It is basically the $y = {x}^{3}$ but narrower. The ends are more upright.

Heads up: If you have a function and its degree is an odd number ie $y = {x}^{3} + 3 x + 5$ so ${x}^{3}$ part or $y = {x}^{5} + 5 x + 247$ so ${x}^{5}$ part or $y = {x}^{7} + 1$ so ${x}^{7}$ part, then you have an odd function. What that means is that the ends of your graph simply point in opposite directions

REMEMBER: At $\left(0 , 0\right)$, make sure you draw it flatter since at that point, it is technically a stationary point of inflexion.

Below is $y = {x}^{5}$

graph{x^5 [-10, 10, -5, 5]}

For comparison, this is $y = {x}^{3}$ (1st graph) and $y = {x}^{11}$ (2nd graph). Notice that at the vertex, it is flatter and the general shape of the graph is narrower

graph{x^3 [-10, 10, -5, 5]}

graph{x^11 [-10, 10, -5, 5]}