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For the curve y = log(x+3)

determine the following:

a) asymptotes, if any.

b) intercepts, if any.

c) domain and range

  • math -

    you should be familiar with the function
    y = log x , which has the y-axis as an asymptote
    this one is simply moved to the left 3 units

    so the vertical asymptote is x = -3
    intercepts :
    for y-intercepts let x = 0 --- y = log3
    for x-intercepts let y = 0
    then log(x+3) = 0
    we know log 1 = 0, so x+3 = 1
    x = -2

    domain: from our definition of logs, x+3 > 0 ---> x > -3
    from knowing the basic graph, the range is any real number.

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