Find all vertical and horizontal asymptotes.Find all vertical and horizontal asymptotes: f ( x ) = 4 x x 2 + 16 My Work: (Vertical)1) x 2 + 16 = 02) x 2 = − 163) not possible so there is no vertical asymptoteMy Work: (Horizontal)1) 4 x / x 2 2) 4/x3) What do I do from here?

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Find all vertical and horizontal asymptotes.Find all vertical and horizontal asymptotes:  f  (  x  )  =            4      x                      x        2            +      16      My Work: (Vertical)1)       x    2    +  16  =  02)       x    2    =  −  163) not possible so there is no vertical asymptoteMy Work: (Horizontal)1)   4  x      /        x    2  2) 4/x3) What do I do from here?

Wischarm1q · Accepted Answer

Vertical asymptote: the only undefined output of f(x) is at x=0. Consider   x  →  0:      lim          x      →      0            (                  4        x                    x        2              +    16    )    =      lim          x      →      0            (          4      x        +    16    )    =  ∞and so x=0 is an asymptote.Horizontal asymptote:      lim          x      →      ∞            (                  4        x                    x        2              +    16    )    =      lim          x      →      ∞            4    x    +  16  =  16and so y=16 is another asymptote.Horizontal asymptote:      lim          x      →      ∞                  4      x                      x        2            +      16        =      lim          x      →      ∞                  4              /            x              1      +      16              /                    x        2              =  0and so y=0 is another asymptote.

Find all vertical and horizontal asymptotes: f(x)=4x/x^2+16 My Work: (Vertical) 1) x^2+16=0 2) x^2=−16 3) not possible so there is no vertical asymptote

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