Algebra 2 Unit Test #1

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Part 1: Calculator Allowed

 1 Rewrite $x<2$ in interval notation. (3)

$x\in \left(-\infty ,2\right)$

 2 Write an interval for the number line shown above. (4)

$x\in \left[-1,5\right)$

 3 Evaluate $f\left(0\right)$ given $f\left(x\right)=\left\{\begin{array}{rr}\hfill -x-4& \hfill x\le -4\\ \hfill -x-3& \hfill -4. (3)

$f\left(0\right)=-\left(0\right)-3=-3$

 4 Find the average rate of change for $f\left(x\right)={x}^{2}+2x+2$ over $x\in \left[-3,-2\right]$. (6)

$f\left(-2\right)={\left(-2\right)}^{2}+2\left(-2\right)+2=2$ and $f\left(-3\right)={\left(-3\right)}^{2}+2\left(-3\right)+2=5$, so the average rate of change is $\frac{2-5}{\left(-2\right)-\left(-3\right)}=\frac{-3}{1}=-3$.

 Algebra 2 Unit Test #1

Part 2: No Calculator Allowed

 5 Rewrite $x\in \left[-1,\infty \right)$ as an inequality. (3)

$x\ge -1$

 6 Identify (by name and equation) the parent function shown above. (3)

Absolute value; $y=\left|x\right|$

 7 Create a table of values and sketch the following equation: $y=-\left|x-1\right|$. (5)

 8 Create a table of values and sketch the following equation: $y=-{x}^{2}+1$. (5)

 9 Create a table of values and sketch the following equation: $f\left(x\right)=\left\{\begin{array}{cc}-x+3& x\le 4\\ {\left(x-5\right)}^{2}& x>4\end{array}\right\$. (5)

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