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1. Evaluating a function by substitution ●○○○○ 10 ptsIf $g(2x - 5) = 3x + 9$ for all real $x$, find $g(1)$.
2. Weighted sum of quadratic values ●○○○○ 10 ptsConsider the function $f(x) = 2x^2 - 4x + 9$. Evaluate $2f(3) + 3f(-3)$.
3. Value of an odd function ●○○○○ 10 ptsThe function $y=f(x)$ is an odd function, and $f(x)=3^x - 1$ for $x \geq 0$. Find $f(-2)$.
4. Odd function value at a positive point ●○○○○ 10 ptsGiven that $f(x)$ is an odd function, and when $x < 0$, $f(x) = x^3 + x^2$, find $f(2)$.
5. Function value from a shifted definition ●○○○○ 10 ptsIf $f(x+1)=x$ for all real $x$, find $f(6)$.
6. Value of an odd function shifted by a constant ●○○○○ 10 ptsGiven that $f(x)$ is an odd function, $g(x)=f(x)+6$, and $g(-1)=3$. Find $f(1)$.
7. Evaluate a function from two values ●●○○○ 20 ptsIf $f(1)=5$, $f(2)=8$ and $f(x)=ax+bx+2$, what is the value of $f(3)$?
8. Piecewise function with equal values ●●●○○ 50 ptsLet $a \neq 0$ be a real number, and define the function $f(x)$ by $$f(x)=\begin{cases}2x+a, & x<1,\\ -x-2a, & x\geq 1.\end{cases}$$ If $f(1-a)=f(1+a)$, find the value of $a$. Give your answer as a decimal.