Pregunta
32 a Sketch the graph of
,
showing clearly the coordinates of
the points where the curve crosses
the coordinate axes and stating
the equations of the
asymptotes.
b The curve with
passes
through the origin. Find the two
possible values of
.
showing clearly the coordinates of
the points where the curve crosses
the coordinate axes and stating
the equations of the
asymptotes.
b The curve with
through the origin. Find the two
possible values of
Ask by Kelly Clark. in the United Kingdom
Jan 04,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
a) Graph of
:
-
Intercepts:
- X-intercepts at
and - No y-intercept
- X-intercepts at
-
Asymptotes:
- Vertical asymptote at
- Horizontal asymptote at
- Vertical asymptote at
b) Values of
for
passing through the origin:
-
and
Solución

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Como
Beyond the Answer
To sketch the graph of
, you start by finding the intersections with the axes. The curve crosses the y-axis at
but note that the x-axis will not be crossed since
is always positive, rendering
negative for all
. The asymptotes occur as
(vertical asymptote) and as
(horizontal asymptote at
).
Now for the second part, to find
when
passes through the origin
, we set the equation to zero:
This leads to:
Rearranging gives
, or
or
. Hence, the two possible values of
are
and
.

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