Sketch the graph of the following function f ( x ) = e − 2 x for x ∈ R this what i got,y-intercept x=0 implies y = 1 e 2 × 0 therefore y=1and I have used the fact that t=−2x → − ∞ as x → ∞by the properties of the Natural Exponential Function: lim x → ∞ e x = ∞ lim x → ∞ e − 2 x = 0 lim x → − ∞ e t = 0 Then I draw the curve graph with y-intercept coordinates (0,1) and approaches zero, but my prof said it's wrong. he commented = e x cannot be zero.

Question

Sketch the graph of the following function  f  (  x  )  =      e          −      2      x       for   x  ∈      R  this what i got,y-intercept x=0 implies   y  =                                                  1                                                                              e                          2              ×              0                                           therefore y=1and I have used the fact that t=−2x   →  −  ∞ as   x  →  ∞by the properties of the Natural Exponential Function:            lim              x        →        ∞                    e      x        =    ∞              lim              x        →        ∞                    e              −        2        x              =    0              lim              x        →        −        ∞                    e              t              =    0  Then I draw the curve graph with y-intercept coordinates (0,1) and approaches zero, but my prof said it&#039;s wrong. he commented =       e    x   cannot be zero.

Laura Fletcher · Accepted Answer

Your professor is correct (as usual) he describes asymptotic behaviour - namely y=0 is a horizontal asymptote for       e          −      2      x      . Sketch the graph of       e          −      2      x       to see this. Firstly you know how to sketch the graph of       e    x   right? You then apply linear transformations which consist of a horizontal reflection in the y-axis and then a stretch of scale factor 1/2 parallel to the x-axis. Does this make sense? If not let me know and I will explain further.

sketch the graph of the following function f(x)=e^−2x for x in R

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New Questions in Calculus 1