Question

For the equation $y=x^3-9x$, determine the intercepts and test for symmetry.

Short answer

The x-intercepts are$(0,0),(3,0),(-3,0)$

Also the function is symmetric

The graph can be given as

Step-by-step solution

Given information

We are given a equation$y=x^3-9x$

We determine the x-intercept

At x-intercept we have $y=0$

On substituting we get

$$\begin{gathered} x^3-9x=0 \\ x(x^2-9)=0 \\ x(x-3)(x+3)=0 \end{gathered}$$

The x-intercepts are$0,3,-3$

Plot the graph

We plot the graph

From the graph we can observe that the graph is symmetric

Conclusion

The x-intercept can be given as $0,3,-3$.

The graph is symmetric

The graph can be given as