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3 problems match “even and odd functions”. Clear

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1. Value of even plus odd function ●●○○○ 20 ptsLet $e(x)$ be an even function and let $o(x)$ be an odd function such that $e(x) + x^2 = o(x)$ for all $x$. Let $f(x) = e(x) + o(x)$. Find $f(2)$.
2. Even function on an interval ●●○○○ 20 ptsLet $f(x)=x^{2}+3ax+4$ be defined on the interval $b-3 \leq x \leq 2b$. Given that $f$ is an even function on this interval, find the value of $a-b$.
3. Sum of values of a shifted odd function ●●●○○ 50 ptsGiven that $f(x)$ is an odd function defined on $\mathbb{R}$ and $f(1) = 1$. If the graph of $f(x)$ is translated one unit to the right, the resulting graph is that of an even function. Find the sum $f(1) + f(2) + f(3) + \ldots + f(2009)$.