How do you find the vertical, horizontal and slant asymptotes of: #y= 2^x#?

1 Answer
Dec 18, 2017

Answer:

This function has one asymptote at #y=0#.

Explanation:

Any function of the form #y=n^x#, where #n# is some number, has a horizontal asymptote where #y=0# because you can't raise a number to any power that will make that original number negative. Like, there is no #x# that exists that could make #n^x# a negative number.

Exponential functions have infinite domains, because there is no number you can put in for #x# that would make #y=2^x# not equal to a real number.
Since there are no #y#-values where the function can't exist, there is no horizontal or slant asymptote.

Note: You can also get the #y#-intercept by plugging #0# in for #x#:
#y=2^0=1#, so the #y#-intercept is at #(0,1)#.
Here's the graph:
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