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Math Help - What does it mean?

  1. #1
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    What does it mean?

    Hi this is a question regarding terminology.

    For the function y = (4^x) - (2^x), find the axes intercepts.

    What does axes intercept mean?

    Thank you!
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  2. #2
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    Re: What does it mean?

    Quote Originally Posted by Tutu View Post
    Hi this is a question regarding terminology.

    For the function y = (4^x) - (2^x), find the axes intercepts.

    What does axes intercept mean?

    Thank you!
    1. If the graph of your function intercepts the x-axis then y = 0;
    if the graph of your function intercepts the y-axis then x = 0.

    Normally you have 2 intercepts (because you have 2 axes)

    2. With your equation

    y = 4^x-2^x = 2^x(2^x-1)

    you easily can see that the graph passes through the origin, that means the x-axis and the y-axis are intercepted simultaneously in one point.

    3. Be aware that the graph of your function has the x-axis as asymptote. ( \lim_{x \to -\infty}(f(x)) = 0)So maybe (depending on the contents of your math lessons) the "improper" point at the left end of the x-axis is called a x-axis intercept too.
    Thanks from Tutu
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  3. #3
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    Re: What does it mean?

    Thanks!

    Sorry could you explain a little more in detail, why the x-axis is the asymptote?

    Also, so can I say that the intercepts are at
    When the curve intersects the x-axis, y=0
    When the curve intersects the y-axis, x-0
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  4. #4
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    Re: What does it mean?

    I suggest you review your basic definitions. An "intercept" is where a graph crosses a specific line- an x-intercept is where the graph crosses the x-axis (and so where y= 0), a y-intercept is where the graph crosses the y- axis (and so where x= 0). An "asyptote" is a straight line that a graph approaches nearer and nearer as at least one of the variables goes to infinity or negative infinity. As earboth pointed out, [tex]y= e^{4x}- e^{2x}= e^{2x}(e^{2x}- 1)[/itex]. What happens as x goes to negative infinity?
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