Pregunta
Graph the rational function.
Start by drawing the vertical and horizontal asymptotes.
Ask by Bernard Mcfarlane. in the United States
Nov 07,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Plot
. Vertical asymptote at
, horizontal asymptote at
.
Solución

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Como
Beyond the Answer
To graph the function
, begin by identifying the vertical and horizontal asymptotes. The vertical asymptote occurs when the denominator is zero, so set
. Solving this gives
. For the horizontal asymptote, since the degree of the numerator (0) is less than the degree of the denominator (1), the horizontal asymptote is
.
Now you can sketch the graph: plot the vertical line at
and the horizontal line at
. The function will approach these lines but never touch them. These asymptotes are essential for understanding the behavior of the graph as
approaches these critical values.
Lastly, plug in a few values of
to get points on the graph, noting that as
approaches -1 from the left,
will trend towards
, and as it approaches from the right, it will trend towards
. To the left of
, the values of
will be negative, and to the right, they will be positive. Happy graphing!

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