Pregunta
For the polynomial function below: (a) List each real zero and its multiplicity. (b) Deter
whether the graph crosses or touches the
-axis at each
-intercept. © Determine the
end behavior.
(a) Find any real zeros of
.
The real zero(s) of
is/are
The multiplicity of the smaller zero is
(Type a whole number.)
The multiplicity of the larger zero is
.
(Type a whole number.)
(b) The graph
the
-axis at the smaller
-intercept.
The graph
the
-axis at the larger
-intercept.
whether the graph crosses or touches the
end behavior.
(a) Find any real zeros of
The real zero(s) of
The multiplicity of the smaller zero is
(Type a whole number.)
The multiplicity of the larger zero is
(Type a whole number.)
(b) The graph
The graph
Ask by Savage Rogers. in the United States
Dec 12,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(a) The real zeros of
are
. The multiplicity of the smaller zero is
. The multiplicity of the larger zero is
.
(b) The graph crosses the -axis at the smaller
-intercept. The graph touches the
-axis at the larger
-intercept.
© As ,
. As
,
.
(b) The graph crosses the
© As
Solución

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Como
The Deep Dive
The real zero(s) of
is/are
and
. The multiplicity of the smaller zero
is
(since it has a factor of
). The multiplicity of the larger zero
is
(as indicated by
).
(b) The graph touches the
-axis at the smaller
-intercept
because of the odd multiplicity. The graph crosses the
-axis at the larger
-intercept
because of the even multiplicity.
For end behavior, as
approaches
,
approaches
because the leading term (from expanding the factors) will be
(positive). Similarly, as
approaches
,
will approach
. So, the end behavior is left descending and right ascending like an isosceles triangle!
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