Algebra 2 Unit Test #1

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Part 1: Calculator Allowed

 1 Rewrite $x>4$ in interval notation. (3)

$x\in \left(4,\infty \right)$

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

$x\in \left(-8,1\right]$

 3 Evaluate $f\left(0\right)$ given $f\left(x\right)=\left\{\begin{array}{rr}\hfill {\left(x+2\right)}^{2}& \hfill x<-1\\ \hfill -x+1& \hfill -13\end{array}\right\$. (3)

$f\left(0\right)=-\left(0\right)+1=1$

 4 Find the average rate of change for $f\left(x\right)={x}^{2}+x+2$ over $x\in \left[-2,0\right]$. (6)

$f\left(-2\right)={\left(-2\right)}^{2}+\left(-2\right)+2=4$ and $f\left(0\right)={\left(0\right)}^{2}+\left(0\right)+2=2$, so the average rate of change is $\frac{2-4}{\left(0\right)-\left(-2\right)}=\frac{-2}{2}=-1$.

 Algebra 2 Unit Test #1

Part 2: No Calculator Allowed

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

$x\le -5$

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

Square root; $y=\sqrt{x}$

 7 Create a table of values and sketch the following equation: $y=-\sqrt{x}-2$. (5)

 8 Create a table of values and sketch the following equation: $y={\left(x-3\right)}^{2}-1$. (5)

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

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