Pregunta
Use transformations to graph the following function. Determine the domain, range,
horizontal asymptote, and
-intercept of the function.
Which transformation is needed to graph the function
? Choose the
correct answer below.
A. The graph of
should be shifted vertically down by 2 units.
C. The graph of
should be shifted horizontally left by 2 units.
D. The graph of
should be shifted horizontally right by 2 units.
horizontal asymptote, and
Which transformation is needed to graph the function
correct answer below.
A. The graph of
C. The graph of
D. The graph of
Ask by Peters Clark. in the United States
Nov 04,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The graph of
should be shifted vertically up by 2 units. The domain is
, the range is
, the horizontal asymptote is
, and the
-intercept is
.
Solución

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Como
Bonus Knowledge
To graph the function
, we begin with the basic exponential function
. The transformation needed here is a vertical shift. Specifically, since the function adds 2, the graph of
should be shifted vertically up by 2 units. So, the correct answer would be none of the options provided, but for clarity: it’s a vertical shift up by 2.
Now, let’s examine the details! The domain of
is all real numbers,
. The range, however, starts just above the vertical shift (2) and extends to infinity, so it’s
. The horizontal asymptote occurs at
since the exponential term approaches zero as
goes to negative infinity. The
-intercept, found by evaluating
, results in
. So, the
-intercept is at
.

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