The table below is drawn for a graph y = x³ - 3x + 1
\(\begin{array}{c|c} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline y = x^3 - 3x + 1 & 1 & -1 & 3 & 1 & -1 & 3 & 1\end{array}\)
From x = -2 to x = 1, the graph crosses the x-axis in the range(s)

Aliyu1679

2 years ago

please explain

Eugene1097

1 year ago

pls explain

Ann_e

1 year ago

We’re given the function:
y=x^3-3x+1

And a table of values (partially reconstructed here):

x y = x³ − 3x + 1
-3 1
-2 ?
-1 3
0 1
1 -1
2 ?
3 1

Let’s compute the missing values:

Calculate y for x = -2:

y=(-2)^3-3(-2)+1=-8+6+2=-1

Now examine sign changes between x-values (i.e., when y changes from + to - or - to +):

Interval y-values Sign change?
-2 to -1 y goes from -1 to 3 Yes (crosses x-axis)
-1 to 0 y goes from 3 to 1 No
0 to 1 y goes from 1 to -1 Yes (crosses x-axis)

So, the graph crosses the x-axis in:
• -2