Pregunta
For the polynomial function below: (a) List each real zero and its multiplicity. (b) Determine
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.
© Select the end behavior of the graph.
A. Falls left and rises right
B. Falls left and right
C. Rises left and right
D. Rises left and falls right
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
© Select the end behavior of the graph.
A. Falls left and rises right
B. Falls left and right
C. Rises left and right
D. Rises left and falls right
Ask by Curry Li. in the United States
Dec 12,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
(a) Real zeros:
(multiplicity 2),
(multiplicity 3)
(b) Graph crosses the -axis at
. Graph touches the
-axis at
.
© End behavior: Falls left and rises right
(b) Graph crosses the
© End behavior: Falls left and rises right
Solución

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Extra Insights
The real zeros of
can be determined by setting the factors equal to zero. Thus, the smaller zero is
with a multiplicity of 3, and the larger zero is
with a multiplicity of 2.
The graph touches the
-axis at the smaller
-intercept
since the multiplicity is odd. It crosses the
-axis at the larger
-intercept
because the multiplicity is even.
For the end behavior: Since the leading term of the polynomial is positive and it is an even-degree polynomial overall, the correct answer is A. Falls left and rises right.
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