The graph of which of the following equations has y = 1 as an asymptote?
O A. y = In(x)
B.
y =
x-1
X
C. y =
xt thing
D. y = e*
E. y = sin(x)

Question

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MrRoyal MrRoyal · Answer 1 · 2021-09-18T18:37:17+02:00

A straight line that approaches the graph without touching; is referred to as an asymptote.

The graph of [tex]y = \frac{x - 1}{x}[/tex] has [tex]y = 1[/tex] as an asymptote

To solve this question, I have attached the graphs of:

[tex]y = \ln(x)[/tex], [tex]y = \frac{x - 1}{x}[/tex], [tex]y =e^x[/tex] and [tex]y = \sin(x)[/tex]

From the attached graphs, we have the following observations

The graphs of [tex]y = \ln(x)[/tex], [tex]y =e^x[/tex] and [tex]y = \sin(x)[/tex] do not have asymptote
The graph of [tex]y = \frac{x - 1}{x}[/tex] has [tex]y = 1[/tex] as an asymptote

Hence, the solution to the question is option (b).

See attachment for the graphs of the four functions