Question

How do you graph `x^3 - 4x + 1` by plotting points?

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^3-4x+1`

To find the y-intercept:

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

`y=0^3-4(0)+1`

`y=1`

Hence, we understand that `color(blue)((0,1)` is the y-intercept of the graph of the given cubic function.

Create a data table with values as shown:

The table below, displays `color(red)((y=1)` when `color(red)((x=0)`

`color(blue)((0,1)` is the y-intercept of the graph of the given cubic function.

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

Solutions for x:

There are three solutions, as `color(red)(f(x)` is a Cubic function.

`color(blue)(x_1 ~~ 1.86081`

`color(blue)(x_2 ~~ -2.11491`

`color(blue)(x_3 ~~ 0.2541`

Hope it helps.