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Math Help - manipulating a function

  1. #1
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    manipulating a function

    f(x) = x^2 + x +1. Find the sum of all values of z for which f(3z) = 7

    Is it 3x^2 +3x + 1 = 7 so z = 1 and -2....so the answer is -1

    also, in general say you have f(x) ....how does the graph change (domain range, intercepts, max, min) if you make it, for example:
    f(-2x)
    .5f(x)
    f(x-2)
    f(x)+2
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by stones44 View Post
    f(x) = x^2 + x +1. Find the sum of all values of z for which f(3z) = 7

    Is it 3x^2 +3x + 1 = 7 so z = 1 and -2....so the answer is -1
    Isomorphism: It is not
    3x^2 +3x + 1 = 7 but (3x)^2 + 3x + 1 = 7. So the equation reads 9x^2 + 3x - 6 = 0, which is 3x^2 + x - 2 = 0

    also, in general say you have f(x) ....how does the graph change (domain range, intercepts, max, min) if you make it, for example:
    f(-2x)
    .5f(x)
    f(x-2)
    f(x)+2
    Do you know what domain, range, intercepts, max,min means. If you know co-ordinate geometry, then express the quadratic as a parabola standard form. This will help you answer all questions easily.
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  3. #3
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    thanks for the first part

    but i am confused..why a quadratic....the function doesnt matter i just wanna know how manipulating inside and outside the perenticies with different operations affects the graph in the form of domain range, min, max and both intercepts
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  4. #4
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    someone please help with the 2nd part...how does each manipulation affect the parts of the equation on a graph? (int. min max, etc.)
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