Pregunta
Summarize all pertinent information obtained by applying the graphing strategy and sketch the graph of
.
Find the domain of
. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The domain is all real
, except
.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Find the
-intercepts of
. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The
-intercept(s) is/are at
.
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no
-intercepts.
Find the
-intercepts of
. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The
-intercept(s) is/are at
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no
-intercepts.
Find the domain of
A. The domain is all real
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
Find the
A. The
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no
Find the
A. The
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
B. There are no
Ask by Bernard Weston. in the United States
Mar 17,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Summary of
:
- Domain: All real numbers except
. -
-Intercept: . -
-Intercept: . - Vertical Asymptote:
. - Horizontal Asymptote:
.
Graph:
- Crosses the
-axis at . - Crosses the
-axis at . - Has a vertical asymptote at
and a horizontal asymptote at .
Solución
Step 1. Factor the function
The given function is
Factor the numerator and denominator:
- Numerator:
- Denominator:
Thus,
This simplifies to
Step 2. Find the Domain
The original denominator
equals zero when
Thus, the domain of
is all real numbers except
.
Domain Answer:
A. The domain is all real , except
.
A. The domain is all real
Step 3. Find the
-intercept(s)
The
-intercepts occur when
. From the simplified form,
the fraction is zero when the numerator equals zero (and the denominator is not zero). Set:
Since
, this is valid.
A. The
Step 4. Find the
-intercept(s)
The
-intercept occurs when
. Substitute
:
A. The
Additional Graphing Information
-
Vertical Asymptote:
The function is undefined when(because the denominator is zero), so there is a vertical asymptote at . -
Horizontal Asymptote:
Since the simplified functionis a rational function of degree 1 in both numerator and denominator, the horizontal asymptote is the ratio of the leading coefficients: -
-Intercept:
The graph crosses the-axis at . -
-Intercept:
The graph crosses the-axis at .
These key elements summarize the graphing strategy for
.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


The Deep Dive
To analyze the function
, we first simplify it. The numerator factors to
, and the denominator factors to
(or
). This gives us
for
.
Domain: The only restriction comes from the denominator. Setting
gives
. Thus, the domain of
is all real
except
:
A. The domain is all real , except
.
A. The domain is all real
X-intercepts: To find the
-intercepts, set
by setting the numerator to zero:
gives
and
. However,
cannot be an
-intercept because it is not in the domain. Therefore, the only
-intercept is:
A. The -intercept(s) is/are at
.
A. The
Y-intercepts: To find the
-intercept, substitute
into the function:
. Thus, the
-intercept is:
A. The -intercept(s) is/are at
.
A. The

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium