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a. suppose that ƒ(x)=axˆ2+bx+c . what must be true about the coefficients if ƒ is an even function?b. suppose that g(x)=axˆ3+bxˆ2+cx+d . what must be true about the coefficients if g is an odd function?
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For even function. f(-x) is the same as f(x). ax2 - bx + c = ax2 + bx + c2bx = 0=> b=0for any function to be ODD :f(-x) = -f(x)-ax3 + bx2 - cx + d = -ax3 - bx2 - cx - d2bx2 + 2d = 0bx2 + d = 0 for all values of x=> b=0=> d=0
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