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2 August, 15:13

What is the vertical asymptote for the function f (x) = ln (x + 4) - 2? Be sure to write your answer as an equation for a line.

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  1. 2 August, 15:43
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    F (x) = ln (x+4) - 2

    Change f (x) to y

    y=ln (x+4) - 2

    Inverse x and y

    x=ln (y+4) - 2

    Solve for y, result will be inverse.

    x+2=ln (y+4)

    convert to exponential form

    e^ (x+2) = y+4

    y=e^ (x+2) - 4

    This is the inverse.

    f^-1 (x) = e^ (x+2) - 4

    Looking at the above function, it is (e^x) shifted to the left by two unit, being brought down (4) units. The only important part of this function is the down-shift of (4), because this represents the horizontal asymptote.

    y = - 4 is the horizontal asymptote, which means

    for f (x) = ln (x+4) - 2

    x=-4 is a vertical asymptotes.
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