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1. Average value of an odd function ●○○○○ 10 ptsFind the average value of $R(z) = \sin(2z)\,e^{1-\cos(2z)}$ on the interval $[-\pi, \pi]$.
2. Evaluating a function by substitution ●○○○○ 10 ptsIf $g(2x - 5) = 3x + 9$ for all real $x$, find $g(1)$.
3. Evaluating a function from its composite form ●○○○○ 10 ptsLet $g(2x + 5) = 4x^2 - 3x + 2$. Find $g(-3)$.
4. Weighted sum of quadratic values ●○○○○ 10 ptsConsider the function $f(x) = 2x^2 - 4x + 9$. Evaluate $2f(3) + 3f(-3)$.
5. Value of a linear expression ●○○○○ 10 ptsIf $7 - 4x = 15$, what is the value of $8x + 2$?
6. Finding a parameter from a known root ●○○○○ 10 ptsIf the solution of the equation $\frac{3}{10}a+\frac{2x+4}{2}=4(x-1)$ is $x=3$, find the value of $a$.
7. Unknown parameter from a root ●○○○○ 10 ptsIf $x=3$ is a root of the equation $\frac{a-2}{x}-\frac{1}{x-2}=0$, find the value of $a$.
8. Limit of a sum with a cube root ●○○○○ 10 ptsCompute $\lim_{x \to 10} \left(4x + \sqrt[3]{x - 2}\right)$.
9. Values of a quadratic at 0, 1, 2 ●○○○○ 10 ptsFor $p(y)=y^2-y+1$, find $p(0)$, $p(1)$ and $p(2)$.
10. Fixed point of a functional definition ●●○○○ 20 ptsLet $h(4x-1) = 2x + 7$ for all real $x$. For what value of $x$ is $h(x) = x$?

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