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

inurbandojoa

inurbandojoa

Answered question

2022-11-08

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=1
and 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.

Answer & Explanation

Laura Fletcher

Laura Fletcher

Beginner2022-11-09Added 22 answers

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.

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