(2x+1)
is a factor of w(x), whose graph is shown. Is the multiplicity of (2x+1)
even or odd?
Option #1: even
Option #2: odd
(1 point)
The multiplicity of (2x+1)
is described by Option #
.
The multiplicity of (2x+1) is described by Option #1: even.
To determine the multiplicity of the factor (2x+1), we need to examine the behavior of the graph where it intersects the x-axis.
If the graph touches and turns around at the x-axis at the point of intersection, then the multiplicity is even. This means that the factor (2x+1) appears as a repeated factor.
If the graph crosses the x-axis at the point of intersection, then the multiplicity is odd. This means that the factor (2x+1) appears as a single factor.
Looking at the given graph, it appears that the graph crosses the x-axis at the point of intersection. Therefore, the multiplicity of (2x+1) is odd.
So, Option #2: odd describes the multiplicity of (2x+1).
To determine the multiplicity of the factor (2x+1), we need to examine the graph of w(x) and look for the behavior around the root -1/2 (which corresponds to the factor (2x+1)).
First, let's understand what multiplicity refers to. In the context of a polynomial function like w(x), the multiplicity of a factor indicates how many times the factor appears as a root of the polynomial.
To find the multiplicity, we need to determine how many times the graph of w(x) touches or crosses the x-axis at the root -1/2 (which corresponds to the factor (2x+1)).
If the graph of w(x) touches or crosses the x-axis at the root -1/2 just once, then the multiplicity of the factor (2x+1) is odd since it would be a single root.
On the other hand, if the graph of w(x) touches or crosses the x-axis at the root -1/2 more than once, then the multiplicity of the factor (2x+1) is even.
Unfortunately, without the given graph, it is not possible to determine how many times the graph crosses or touches the x-axis at the root -1/2. Hence, we cannot determine the multiplicity of the factor (2x+1) using the available information.
Therefore, the answer cannot be determined from the provided information, and Option #3: uncertain would be the appropriate response.