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Math Help - Need help with Calculus Packet

  1. #1
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    Need help with Calculus Packet

    I have a calculus packet to do over the summer. I did as much as i could but i really didn't know how to do a few questions.

    1. Find a formula for the function f graphed below
    (theres a graph with the points (0,0)(1,1)(2,0)(3,0)(4,0)(5,0)

    2. Let f and g be odd functions. If p,r, and s are nonzero functions defined as follows, which must be odd?
    I. p(x)=f(g(x)) II. r(x)=f(x)+g(x) III. s(x)=f(x)*g(x)
    (A) I only; (B) II only; (C) I and II only; (D) II and III only; (E) I, II, and III

    3. The graphs of f and g are shown below and h=f g. Estimate the value of h(0.5). Then sketch the value of h



    Any help is greatly appreciated
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sanghoon93 View Post
    3. The graphs of f and g are shown below and h=f g. Estimate the value of h(0.5). Then sketch the value of h



    Any help is greatly appreciated
    h(x)=(f \circ g)(x)=f(g(x))

    So to evaluate h(0.5) look up the value of g(0.5) and lets call that u, then look up f(u).

    CB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by sanghoon93 View Post
    2. Let f and g be odd functions. If p,r, and s are nonzero functions defined as follows, which must be odd?

    I. p(x)=f(g(x))

    II. r(x)=f(x)+g(x)

    III. s(x)=f(x)*g(x)


    (A) I only; (B) II only; (C) I and II only; (D) II and III only; (E) I, II, and III
    The defining property for a function h(x) to be odd is that h(-x)=-h(x).

    Now for each of the given functions you need to determine if this property holds. I will do I. for you:

     <br />
p(x)=f(g(x))<br />

    so:

     <br />
p(-x)=f(g(-x))<br />

    but g is odd so g(-x)=-g(x) hence:

    p(-x)=f(-g(x))

    but f is also odd so:

    p(-x)=-f(g(x))=-p(x)

    and so p is odd.

    CB
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