Why does f(x) = x^(-n) for n>0 have both hor. asymptote (x-axis) and vert. asymptote?

[mkh0419]

Why does f(x) = x^(-n) for n>0 have both hor. asymptote (x-axis) and vert. asymptote?

Hello,

Why does f(x) = x^(-n) for n>0 have both a horizontal asymptote (x-axis) and a vertical asymptote (y-axis)?

Thank you very much!

 

[Deleted member 4993]

Hello,

Why does f(x) = x^(-n) for n>0 have both a horizontal asymptote (x-axis) and a vertical asymptote (y-axis)?

Thank you very much!

Under what condition/s, a function can have a vertical asymptote?

Under what condition/s, a function can have a horizontal asymptote?

 

[stapel]

Why does f(x) = x^(-n) for n>0 have both a horizontal asymptote (x-axis) and a vertical asymptote (y-axis)?

Try using what you learned back in algebra:

Since the index n is positive, then the power -n is negative. What kinds of graphs did you get when you were sketching y = x^-3, y = x^-4, etc? (here)

Since a negative power means "flip the base to the other side of the fraction" (here), think about what you got when you graphed y = 1/x³, y = 1/x⁴, etc.

Think about what they taught you about why one might have vertical asymptotes, and how one figures out horizontal (or slant) asymptotes for rational functions. (here)