Question

Graph the function f(x) = x3 – 4x – 1. Which are approximate solutions for x when f(x) = 0? Check all that apply. –2.11 –1.86 –0.25 0.25 1.86 2.11

Answer 1

The solutions to this will be found where the graph goes through the x-axis...when y = 0.  Since f(x) and "y =" are interchangeable, this makes sense.  When you graph it and use your "trace" button you will find that the solutions are -1.8608, -.254102, and 2.11491

Answer 2

Answer:

-1.86, -0.25 and 2.11

Step-by-step explanation:

In the figure  attached a plot of the function is shown. The solutions for x when f(x) = 0 are also given.

To check if a given x is solution of f(x) = 0, just replace x value in the formula and verify if the function is or not equal to zero.

x           f(x)

-2.11      (-2.11)^3 - 4(-2.11) -1 = -1.95

-1.86     (-1.86)^3 - 4(-1.86) -1 ≅ 0

-0.25    (-0.25)^3 - 4(-0.25) -1 ≅ 0

0.25     (0.25)^3 - 4(0.25) -1 = -1.98

1.86      (1.86)^3 - 4(1.86) -1 = -2

2.11       (2.11)^3 - 4(2.11) -1 ≅ 0

Therefore, the solutions are: -1.86, -0.25 and 2.11