# How do you graph #f(x)=2-x^3# using zeros and end behavior?

##### 1 Answer

Left end is upwards, right end is downwards, and the graph crosses the x-axis at

#### Explanation:

This function

Since this is a degree 3 polynomial, the odd degree (3) tells us that the left and right ends of the graph will point in opposite directions.

The leading coefficient is -1, which indicates that the right end of the graph will point downwards. (Hint: the negative leading coefficient means the right tail points towards the negative

Next we should check for both

The rough sketch using just this information should behave following these patterns:

- The graph comes down from the top of the graph paper on the left side of the y-axis.
- The graph crosses over the y-axis at (0,2), and heads towards the x-axis.
- The graph crosses over the x-axis at
#(root(3)(2),0)# heading downwards. - The graph exits off the bottom of the graph paper to the right of
#x=root(3)(2)#

Here's how it looks:

graph{2-x^3 [-4.656, 5.21, -0.705, 4.228]}