Question 1001042
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Below is the plot of the functions  y1 = {{{5 + e^(-x^2)}}}  (in red)  and  y2 = {{{e^(-x^2)}}}  (in green)  with the horizontal asymptote  y = 5  (in blue).

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{{{graph( 330, 330, -3.5, 3.5, -1.5, 8.5,
          5 + e^(-x^2),
          e^(-x^2), 5
)}}}


<B>Figure</B>. Plots y1 = {{{5 + e^(-x^2)}}} and y2 = {{{e^(-x^2)}}}

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The function &nbsp;y2 = {{{e^(-x^2)}}} &nbsp;tends to zero at &nbsp;x ---> +/-{{{infinity}}}.


Therefore, &nbsp;the function &nbsp;y1 = {{{5 + e^(-x^2)}}} &nbsp;tends to &nbsp;5 at &nbsp;x ---> +/-{{{infinity}}}.


y = 5 &nbsp;is the horizontal asymptote for the function &nbsp;y1.


Notice that the function &nbsp;y1 &nbsp;is not a rational function, &nbsp;as well as the function &nbsp;y2.