At root x = 0, the graph of the function crosses the x-axis.
How to determine at which roots the graph of a function crosses the x-axis
To determine at which roots the graph of a function crosses the x-axis, we need to find the values of x for which the function equals zero.
Given the roots 0, -2, -4, and 5, evaluate the function at these values to determine if it equals zero:
For x = 0:
Substitute x = 0 into the function and check if it equals zero:
The graph crosses the x-axis at x = 0.
For x = -2:
Substitute x = -2 into the function and check if it equals zero:
f(-2) = (4(-2) - 2
) / (-2 - 2) = (-8 - 8) / (-4) = -16 / (-4) = 4
The graph does not cross the x-axis at x = -2.
For x = -4:
Substitute x = -4 into the function and check if it equals zero:
f(-4) = (4(-4) - 2
) / (-4 - 2) = (-16 - 32) / (-6) = -48 / (-6) = 8
The graph does not cross the x-axis at x = -4.
For x = 5:
Substitute x = 5 into the function and check if it equals zero:
f(5) = (4(5) - 2
) / (5 - 2) = (20 - 50) / 3 = -30 / 3 = -10
The graph does not cross the x-axis at x = 5.
Therefore, the graph of the function crosses the x-axis at x = 0. It does not cross the x-axis at x = -2, -4, or 5.