Find the Asymptotes f(x)=1/x

Problem

ƒ(x)=1/x

Solution

1. Identify the vertical asymptote by finding the values of x where the denominator is zero and the numerator is non-zero.

2. Set the denominator equal to zero.

x=0

3. Check the limit as x approaches 0 to confirm the vertical asymptote.

(lim_x→0)(1/x)=±∞

4. Identify the horizontal asymptote by finding the limit of the function as x approaches infinity or negative infinity.

(lim_x→∞)(1/x)=0

5. Conclude that the horizontal asymptote is the line where the function value stabilizes.

y=0

Final Answer

Vertical Asymptote: *x=0, Horizontal Asymptote: *y=0

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