How do you graph $x^{3} - 4 x + 1$ $x^3 - 4x + 1$ by plotting points?

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Answer 1 · 2018-07-24T23:46:21

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Please read the explanation.

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We are given the Cubic Function: $y = f (x) = x^{3} - 4 x + 1$ $color(red)(y=f(x)=x^3-4x+1$

To find the y-intercept:

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

$y = 0^{3} - 4 (0) + 1$ $y=0^3-4(0)+1$

$y = 1$ $y=1$

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

Create a data table with values as shown:

enter image source here

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

enter image source here

$(0, 1)$ $color(blue)((0,1)$ 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:

enter image source here

Solutions for x:

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

$x_{1} \approx 1.86081$ $color(blue)(x_1 ~~ 1.86081$

$x_{2} \approx - 2.11491$ $color(blue)(x_2 ~~ -2.11491$

$x_{3} \approx 0.2541$ $color(blue)(x_3 ~~ 0.2541$

Hope it helps.

How do you graph x^3 - 4x + 1x3−4x+1x^3 - 4x + 1 by plotting points?