Consider the graph of m(x). Given that (x−4)
is a factor of m(x), is the multiplicity of (x−4)
even or odd?
Option #1: even
Option #2: odd
(1 point)
The multiplicity of (x−4)
is described by Option #
.
Option #2: odd
To determine the multiplicity of the factor (x-4) in the graph of m(x), we need to examine the behavior of the graph near the x = 4 point.
If the graph crosses the x-axis at x = 4, then the multiplicity of the factor (x-4) would be odd. This means the graph would have to pass through the x = 4 point.
If the graph touches but does not cross the x-axis at x = 4, then the multiplicity of the factor (x-4) would be even. This means the graph would bounce off the x = 4 point without crossing it.
Considering these options, the description that best fits the given information is Option #2: odd.
To determine the multiplicity of the factor (x-4) in the function m(x), we need to analyze the graph of m(x) near the point x=4. The multiplicity of a factor represents how many times it appears in the factored form of the function.
To find the multiplicity, follow these steps:
1. Look at the graph near the point x=4.
2. If the graph touches or crosses the x-axis at x=4 and continues in the same direction, the multiplicity is odd.
3. If the graph touches or crosses the x-axis at x=4 and changes direction, the multiplicity is even.
So, observe the behavior of the graph near x=4. If it touches or crosses the x-axis and continues in the same direction, the multiplicity is odd. If it touches or crosses the x-axis and changes direction, the multiplicity is even.
Based on the information provided, we cannot determine the behavior of the graph near x=4 and whether it touches or crosses the x-axis. Therefore, we cannot determine whether the multiplicity of (x-4) is even or odd.
Option #3: Unable to determine.