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Math Help - Prerequisite for calc

  1. #1
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    Prerequisite for calc

    just a couple problems i need help with, they're in chapter 1 of my calculus book, it's like reviewing for calculus i suppose you could say.

    Determine whether the graph of the function is symmetric about they y-axis, the origin, or neither.

    1. y= x ^ 1/5

    2. y=x^2 -2x - 1

    ... also

    find the domain and range
    1. y= |x|-2
    2. y=ln(x-3)+1
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  2. #2
    MHF Contributor Calculus26's Avatar
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    A fn is symmetric about the y axis if f(-x) = f(x)

    in other words if you replace x with -x you get the same formula

    For eg y = x^2 = (-x)^2

    for y= x^(1/5) -> (-x)^1/5 = -x^(1/5) so it is not symmetric about yaxis

    if f(-x) = - f(x) then the fn is symmetric wrt the origin

    again this means if you replace x with -x you get -y

    for y= x^(1/5) -> (-x)^1/5 = -x^(1/5) = - y

    if neither happens you get neither I'll leave the second for you to do

    For the domain and range :

    y = |x| -2 the domain of |x| is all x and the range is [0,inf)

    so for |x| - 2 it is simply a vertical shift of 2 units down so the range

    is [-2,inf)

    For ln(x) the domain is (0,inf) so ln(x-3) is a horizontal shift to the right
    3 so the domain is (3,inf) or if you will the domain is x-3 >0 or x>3


    For ln(x) the range is (-inf,inf) so what does adding +1 to the range do?
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