At which root does the graph of f(x) = (x + 4)^6(x + 7)^5 cross the x axis?
2 answers:
ANSWER
The graph of
crosses the x-axis at
EXPLANATION
The nature of the multiplicity of a given polynomial function determines whether the graph crosses the x-axis at that intercept or not?
If the multiplicity of the factor is even as in
the graph touches but does not cross the x-axis at the intercept where
This means that the x-axis is a tangent to the function at this point.
However, if the multiplicity is odd, as in
the graph crosses the x-axis at the intercept where
The graph of
crosses the x-axis at
EXPLANATION
The nature of the multiplicity of a given polynomial function determines whether the graph crosses the x-axis at that intercept or not?
If the multiplicity of the factor is even as in
the graph touches but does not cross the x-axis at the intercept where
This means that the x-axis is a tangent to the function at this point.
However, if the multiplicity is odd, as in
the graph crosses the x-axis at the intercept where
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