Pregunta
Given:
5.2.1 Determine the coordinates of the
-intercept of
.
5.2.2 Explain why
does not have an
-intercept.
5.2.3 Draw a sketch graph of
, clearly showing all asymptotes, intercepts with the axes and at least one other point on
.
5.2.4 Describe the transformation from
to
if
.
5.2.1 Determine the coordinates of the
5.2.2 Explain why
5.2.3 Draw a sketch graph of
5.2.4 Describe the transformation from
Ask by Reese Hobbs. in South Africa
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
- The
-intercept of is at . -
does not have an -intercept because is always greater than 0. - The graph of
has a horizontal asymptote at and passes through points like and . - Function
is obtained by shifting vertically upward by 7 units.
Solución

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Como
Bonus Knowledge
To find the
-intercept of
, evaluate
:
So, the coordinates of the
-intercept are
.
The function
approaches 1 as
because
gets closer to 0, but it will never reach 0. Consequently,
will never cross the
-axis since it is bounded below by 1 and will never equal 0.
To sketch the graph of
, start with the horizontal asymptote at
. Mark the
-intercept at
. As
decreases,
will increase toward infinity. You can choose another point, like
, to illustrate the function’s behavior.
Transforming from
to
involves analyzing the function alteration. The function
can be rewritten, revealing two transformations: first, an upward shift by 8 units and then applying the same vertical scaling of 4. Hence, the core behavior of
rises significantly compared to
.

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