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Homework Help: What is the asympote of this graph?

  1. Aug 17, 2010 #1
    1. The problem statement, all variables and given/known data

    How come the graph of y = 2^x has a negative x-axis as an asympote. And what is the asympote of this graph?

    2. Relevant equations

    An asympote is a line that approaches the graph but does not intersect as x increases or decreases.

    3. The attempt at a solution

    I know the graph of y = 1/2^x has an asympote which is y = 0 because its closer to the y=0. But for y= 2^x, i only see the numbers increasing, would the asympote be y = - 2
     
  2. jcsd
  3. Aug 17, 2010 #2

    Mark44

    Staff: Mentor

    Re: Asympote

    Because as x gets more and more negative, y = 2^x gets closer to zero. The horizontal asymptote is the line y = 0.
    I think you have this backwards. An asymptote is a line that the graph approaches. A curve can intersect or cross a horizontal asymptote for values of |x| that are relatively small, but won't intersect or cross when x is large or is very negative.
    y = 2^x is defined for all real numbers x. You're focusing on large values of x. The curve is asymptotic to the x-axis for x approaching -infinity. The graphs of y = 2^x and y = 2^(-x) are reflections of each other across the y-axis, so if one has the positive x-axis as its horizontal asymptote (y = 2^(-x) = 1/2^x), the other will have the negative x-axis as its horizontal asymptote.
     
  4. Aug 17, 2010 #3
    Re: Asympote

    in the graph 2^x, doesn't matter what value for x, y NEVER can be zero or negative, because this is exponential relation. try x=-100000000, y is extremely small but can never be zero. The asymptote for that graph is y=0, where y can never approach value closer to zero.
     
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