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Math Help - Urgent basic calculus help needed...(this wasn't covered in class notes!)

  1. #1
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    Urgent basic calculus help needed...(this wasn't covered in class notes!)

    1) Given f(x) = 3x + 2, where is the function increasing?

    2) Given f(x) = x-2 / 3
    The "/" is meant to denote a fraction, x-2 over 3
    -what is the vertical asymptote?
    -what is the horizontal asymptote?


    THANKS SO MUCH IN ADVANCE!
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  2. #2
    o_O
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    1. What does the graph of this look like? You should be able to figure out quickly that it's ALWAYS increasing. Why? Look at f'(x)

    2. f(x) = \frac{x-2}{3}
    Vertical asymptote: Is there even any x values that f(x) cannot have (i.e. lead to a division of 0 or anything like that?)?

    Horizontal asymptote: You should tell what type of graph this is and deduce if there are any. But nonetheless, what is: \lim_{x \to \pm \infty} f(x)?
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  3. #3
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    Quote Originally Posted by o_O View Post
    1. What does the graph of this look like? You should be able to figure out quickly that it's ALWAYS increasing. Why? Look at f'(x)

    2. f(x) = \frac{x-2}{3}
    Vertical asymptote: Is there even any x values that f(x) cannot have (i.e. lead to a division of 0 or anything like that?)?

    Horizontal asymptote: You should tell what type of graph this is and deduce if there are any. But nonetheless, what is: \lim_{x \to \pm \infty} f(x)?
    Thanks for the input, this is what I came up with:

    For (1) I came up the function is increasing at negative infiniti.
    For (2) I came up with where is no vertical asymptote and no horizontal asymptote.

    Do those answers sound right?
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  4. #4
    o_O
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    2 is correct.

    For the first one, what kind of graph is it? What is f'(x)? If a function is monotonically increasing, what property should f'(x) have?
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  5. #5
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    Quote Originally Posted by o_O View Post
    2 is correct.

    For the first one, what kind of graph is it? What is f'(x)? If a function is monotonically increasing, what property should f'(x) have?
    Wait...f'(x) is negative, therefore it is increasing NOWHERE?
    ps - please excuse my stupidity..I haven't taken a math course in years, I'm only doing this so I can get into med school.
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  6. #6
    a.a
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    a reali easy way to look at #1 is that its a striaght line with a +ve sope.. so that means it is increasing

    also f'(x)= 3... a +ve number..
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