Determine the end behavior of the following transcendental functions by

iohanetc

iohanetc

Answered question

2021-10-13

By examining the appropriate limits, ascertain the final behavior of the following transcendental functions. The associated graph is then simply sketched, with any asymptotes indicated.
f(x)=2x

Answer & Explanation

2abehn

2abehn

Skilled2021-10-14Added 88 answers

Step 1
To determine the end behavior of the following transcendental functions by analyzing appropriate limits.
Given function is f(x)=2x
To find end behavior of function f(x)=2x we have to find asymptotes for f(x)=2x
1) To find horizontal asymptotes:
The line y=L is a horizontal asymptote of the function y=f(x) if either
limxf(x)=L or limxf(x)=L
and L is finite.
Now here,
limx2x=2=
and limx2x=2=0
Therefore the line y=0 is the horizontal asymptote for f(x)=2x
Step 2
2) To find vertical asymptotes:
The line x=L is a vertical asymptote of the function f(x)=2x if the limit of the function at this point is infinite.
Here the function f(x)=2x is defined for every value of x.
Therefore there are no vertical asymptotes for f(x)=2x
3) To find slant asymptotes:
The line y=mx+b is slant asymptote of a function y=f(x) if either m=limx(f(x)x)=L or
m=limx(f(x)x)=L and L is finite and zero
m=limx(f(x)x)=limx2xx=
and m=limx(f(x)x)=limx2xx=0
Here the value of L is not finite and non zero.
Therefore the function f(x)=2x has no slant asymptotes.
Step 3
The sketch of the graph of function f(x)=2x is,
image

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