algebra

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determine the domain, range and horizontal asymptote Please show all your work
f(x) = - (3/4)^x - 1
Help!

  • algebra -

    domain : any real value for x
    range : y > -1

    horizontal asymtote: y = -1

    domain and range, just look at a sketch of the graph

    last part:
    intuitively, as x --> ∞+ , value of (3/4)^x --> 0
    ( e.g. (3/4)^100 = 3.2 x 10^-13 , pretty close to zero)

    as x -- > -∞
    we get (3/4)^-x
    = (4/3)^ +x ---> ∞

    so look at x --> +∞
    f(x) --> 0 - 1 = -1
    so y = -1 is the horizontal asymtote

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