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College Calculus

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The graph A(x) has points (-3,0), (0,-2), (1,0) and (2,3).

If C(x) is defined by C(x)=A(2x+3), then what is the domain and range of C and how would the graph of C(x) look like?

Also, is there any way to find what the actual equation of A(x) is with the points listed above? Thank you for the help!

  • College Calculus - ,

    consider A(x) = Ax^3+Bx^2+cx + D

    A(-3)=0=-27A+9B-3C + D
    A(0)=-2=D that is nice
    A(1)=0=A+B+C+D
    A(2)=....

    so you can solve for the four constants A,B,C,D and you have an equation that fits the points....if all the points are allowed in the domain.

    If C(x)=A(2x+3) domain is all values of x , and range is all numbers.

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