Question

How do you graph `f(x) = x^3-2x-4`?

Answer 1

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Please read the explanation.

Explanation:

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We are given the Cubic Function: `color(red)(y=f(x)=x^3-2x-4`

To find the y-intercept:

Set `color(blue)((x=0)` to find the corresponding of `color(blue)((y))`

`y=0^3-2(0)-4`

`y=(-4)`

Hence, we understand that `color(blue)((0,-4)` is the y-intercept of the graph of the given cubic function.

To find the x-intercept:

Set `color(blue)((y=0)` to find the corresponding of `color(blue)((x))`

`0=x^3-2(x)-4`

We are unable to factor the cubic function above.

Create a data table with values as shown:

The table on the right hand side, displays `color(red)((y=-4)` when `color(red)((x=0)`

`color(blue)((0,-4)` is the y-intercept of the graph of the given cubic function.

In the table, we can also observe that `color(red)((y=0)` when `color(red)((x=2)`

`color(blue)((2,0)` is one of the x-intercepts of the graph of the given cubic function.

Using an appropriate graphic software or a calculator, we can obtain the graph as shown below:

Hope it helps.