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$8$ $\left(1$ Point) $1\right)$ The\ reciprocal\\ $0+11\right)$ \left(\frac{2} $c\left(2\right)$ {5}\right)^0\ $\right)$ \ $1111s\right)$ $S$ $S1S$ $s3S$ $S4S$ $s2S$

a) (6 points) Find the standard form $f\left(x\right)=a\left(x-h\right)^{2}+k$ b) (5 points) Fill in the blanks. For quadratic function f, its figure is opening $\left(l1pWard/d0WnWa$ $d\right)$ it has $\left(minimlm/max1mlm\right)$ its vertex is ( the axis of $f1sx=$ 5. (14 points) Find the inverse function $\bar{f^{-1}0f} $ $f\left(x\right)=\dfrac {2x-5} {3x+1}$ then find the range of f in interval. function 6. (11 points) Graph the polynomial $f\left(x\right)=\left(x+2\right)\left(x+1\right)^{2}\left(x-1\right)\left(x-2\right)^{2}$ To receive full credit, sketch all the $x-and$ 7. (13 points) Complete transformations needed $cep5$ $1cnc0nneCtlem$ $y$ $0my=f\left(x\right)t0y=-2f\left(\dfrac {7} {2}^{0pe}$ $+$ $2\right)-5in$ the given order. a) Shift $\left(lef/right\right)by$ b) $\left(Compress/Sttretch\right)$ horizontally by (x/y) axis. c) Reflect about $\left(Compress/Sttretch\right)$ vertically by d) e) Shift $\left(lp/d0Mn\right)$ by 8. (14 points) Find quotient and remainder when divide $x^{5}+2x^{3}-2x^{2}+x-7mithx^{2}+2$ 9. $\left(BONJS$ 20 points) Find $f\left(x\right)=x^{5}-12x^{4}+55x^{3}-120x^{2}+124x-48$ with known zeros $x=1,2$ $End0fTest\infty 0$

its vertex is ( the axis of f $1sx=$ 5. (14 points) Find the inverse function $\bar{f^{-1}0f} $ $f\left(x\right)=\dfrac {2x-5} {3x+1}$ then find the range of f in interval. function 6. (11 points) Graph the polynomial $f\left(x\right)=\left(x+2\right)\left(x+1\right)^{2}\left(x-1\right)\left(x-2\right)^{2}$ To receive full credit, sketch all the $x-and$ $y-lnterCepts$ 7. $\left(13$ points) Complete transformations needed from $ccp5$ $lnenconnectl$ $cm$ $10peny$ $ny=f\left(x\right)t0y=-2f\left(2+2\right)-5in$ the given ordes by a) Shift $\left(lef/r1ght\right)$ $\left(Compress/Stretch\right)$ horizontally by b) $\left(x/y\right)$ axis. c) Reflect about $\left(Compress/Stretch\right)$ vertically by d) e) Shift $\left(lp/doMn\right)$ by 8. (14 points) Find quotient and remainder when divide $x^{5}+2x^{3}-2x^{2}+x-7miihx^{2}+2$ 9. (BONUS, 20 points) Find $f\left(x\right)=x^{5}-12x^{4}+55x^{3}-120x^{2}+124x-48$ $Mitb$ known zeros $x=1,2$ e $End0fTest90$

The is the statement of the Mean Value Theorem from your $te\times tb00k$ $Tneoren$ $m4.5$ $Ne8n$ Value Theorem Let f be continuous over $leclose$ interval $\left(a.b\right)aod$ $i$ $eo$ $xd$ $csnlc$ $\left(ab\right)$ $mmd$ exists at least one point cE $\left(a.b\right)$ $si1dhtba$ $f^{'}\left(c\right)=\dfrac {f\left(b\right)-f\left(a\right)} {b-a}$ What is the geometric interpretation of the conclusion of the theorem? O The tangent line to the graph of \(f\left(x\right)\) at $l\left(c1\right)$ is parallel to the secant line connecting \(\left(a,f\left(a\right)\right)\) and \(\left(b,f\left(b\right)\right)\). O The tangent line to the graph of $\left(f\left(lef\left(x\left(right\right)$ at \(c\) is the secant line connecting \(\left(a,f\left(a\right)\right)\) $ana$ \(\left(b,f\left(b\right)\right)\). O The tangent line to the graph $of$ $\left(f\left(leF\left(x\left(right\right)\left(\right)at1\left(c1\right)is$ perpendicular to the secant line connecting \(\left(a,f\left(a\right)\right)\) and A(\left(b,f\left(b\right)\right)\). O The tangent line to the graph of $\left(fleH\left(x\right)nght\right)\right)\right)$ $at$ $\left(c\right)\right)ishoizonta|$ $Tnere$ is more than one tangent line to the graph $0no$ $\left(flcf\left(x\right)night\right)\left($ $at1\left(c1\right)$

$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ $s1S$ $S-1S$ $s2S$ $s50s$

Which of the following rational numbers are equivalent? $0Ptionsy$ A \frac{5}{6}, \frac{30}{36} B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ D \frac{1}{2},\frac{3}{8}