(Solved): \( 100 \% \) completion of this worksheet will give you 300 pts on daily assignments Find all zeros ...

\( 100 \% \) completion of this worksheet will give you 300 pts on daily assignments Find all zeros. 1) \( f(x)=(2 x-1)(x-5) \) 2) \( f(x)=(x-3)(3 x+1)(x+1) \) 3) \( f(x)=(2 x+1)(x+1)(x-1) \) Write a polynomial function of least degree with integral cocfficients that has the given zeros. 9) \( 3,2,-2 \) 10) 3, \( 1,-2,-4 \) Identify the leading coefficient, degree, and end behavior. 1. \( f(x)=5 x^{2}+7 x-3 \) 2. \( y=-2 x^{2}-3 x+4 \) 3. \( g(x)=x^{3}-9 x^{2}+2 x+6 \) Degret: Degree: Degree: Leading Coeft: Leading Coeff: Leading Coeff: Find Behavior: End Behavior: End Behavio: 4. \( y=-7 x^{3}+3 x^{2}+12 x-1 \) 5. \( h(x)=-2 x^{7}+5 x^{4}-3 x \) 6. \( g(x)=8 x^{3}+4 x^{2}+7 x^{4}-9 x \) Degres: Degree: Degree: Leading Coeff: Leading Coeff: Leading Coeff: Find Behavior: Find Behavior: End Behavior: Identify whether the function graphed has an odd or even degree and a positive or negative leading cocfficient. Justify your answer. 10. 11. 12, jedify: jusify: justify: State the zeros, end behavior and sketch a possible graph that fits the information obtained. 1) \( y=(x-5)^{2}(x+2)(x+5)^{2} \) 2) \( y=(x-2)(x+4)^{2}(x-5) \) Zeros: Zeros: F.R F. \( \mathbf{R} \). Simplify each expression. 1) \( \frac{35 n}{35 n^{2}} \) 2) \( \frac{45 x^{2}}{25 x} \) 3) \( \frac{x-8}{x^{2}+x-72} \) 4) \( \frac{p^{2}-3 p-54}{p-9} \) Name: Class period: 5) \( y=-x(x-5)^{2}(x-2)(x+6) \) 6) \( y=-(x-1)^{2}(x-5)(x+5)^{2} \) Zeros: Zeros: E n : E \( \mathbf{n} \) : Divide using synthetic division: 5. \( \left(x^{2}+x+30\right)+(x+3) \) 6. \( \left(x^{2}-2 x-10\right)+(x+5) \) \( \mathrm{b}(x+3) \) a factor of \( \left(x^{2}+x+30\right) ? \) Ls \( (x+5) \) a factor of \( \left(x^{2}-2 x-10\right) \) ? 7. \( \left(x^{3}-3 x^{2}-16 x-12\right)+(x-6) \) 8. \( \left(x^{4}-7 x^{2}-18\right)+(x+3) \) Is \( (x-6) \) a factor of \( \left(x^{3}-3 x^{2}-16 x-12\right) ? \) h \( (x+3) \) a factor of \( \left(x^{4}-7 x^{2}-18\right) \) ? Name: Class period: 9) \( \frac{v^{2}+7 v-30}{9 v^{2}+90 v} \) 10) \( \frac{b^{2}+b-30}{3 b^{2}+18 b} \) 11) \( \frac{3 x^{2}+5 x-2}{7 x^{2}+12 x-4} \) 12) \( \frac{3 b^{2}+26 b-9}{5 b^{2}+40 b-45} \) Identify the holes, vertical asy mptotes, \( x \)-intercepts, herirontal asymptote, and domain of each. Then sketch the graph. 1) \( f(x)=\frac{4}{x-3} \) 2) \( f(x)=\frac{x^{2}+7 x+12}{-2 x^{2}-2 x+12} \) 5) \( f(x)=\frac{-2 x^{2}+4 x+16}{x^{2}-5 x+4} \) 6) \( f(x)=\frac{x^{2}-3 x}{2 x^{2}+2 x-12} \) 7) \( f(x)=\frac{3 x+6}{x+3} \) 8) \( f(x)=\frac{x^{2}+5 x+4}{x^{2}-1} \) 3) Write the equation for the function that results from each transformation applied to the base ful \( y=5^{x} \) a) translate down 3 units b) shift right 2 units c) translate left \( \frac{1}{2} \) unit d) shift up 1 unit and left \( 2.5 \) units 4) Describe the transformations that map the function \( y=8^{x} \) onto each function. a) \( y=\left(\frac{1}{2}\right) 8^{x} \) b) \( y=8^{4 x} \) c) \( y=-8^{x} \) d) \( y=8^{-2 x} \) 5) Write the equation for the function that results from each transformation applied to the base function \( y=7^{x} \) a) reflect in the \( x \)-axis (vertical reflection) b) stretch vertically by a factor of 3 c) stretch horizontally by a factor of \( 2.4 \) d) reflect in the \( y \)-axis and stretch vertically by bafo 7 6) Sketch the graph of \( y=\left(-\frac{1}{2}\right) 2^{x-4} \) by using \( y=2^{x} \) as the base and applying transformations. 1. \( y=12000-(1+0.3)^{\prime} \) A. Does this function represent exponential B. What is your inital value? C. What is the rate of growth or growth or exponential decay? race of decay? 2. \( y=55 \cdot(1-0.02 \gamma \) A. Does this function represent exponential 8. What is your initial value? C. What is the rate of prowth or growth or exponential decay? me of decay? 3. \( y=100 \cdot(1.25)^{\prime} \) A. Does this function represent exponential B. What is your inctal value? C. What is the rate of growth or growth or exponential decoy? rate of decay? 5. \( y=2000-(1,05)^{\prime} \) A. Does this function represent exponential B. What is your intal value? C. What is the rate of growth of zrowth or exponemial decay? rate of decay? 6. \( y=14000-(0.92 Y \) A. Does this function represent exponential B. What is your intal value? C. What is the rate of growth or growth or exponential decay? rate of decay? 9. The first year of a charity walk event had an attendance of 500 . The attendance \( y \) increases by \( 5 \% \) each year, A. Write an exponential growth function to represent B. How many people will attend in the 10th year? this situation. Round your answer to the nearest person. 10. The population of a small tewn was 3600 in 2005 . The population increases by 4 ts annually. A. Write an exponential growth function to represent B. What will the population be in 2025? mound your this situation. ansaer to the nearest person 11. Your starting salary at a new company is \( \$ 34,000 \) and it increase by \( 2.5 \% \) each year. A. Write an exponential growth function to represent B. What will you salary be in 5 years? Round your this satuation. answer to the nearest dollar. 12. In 2010 an item cost \( \$ 9.00 \). The price increase by \( 1.5 \% \) each year. A. Write an exponential growth function to represent B. How much will it cost in \( 2030 ? \) Round your answer to this situation. the nearest cent. 13. The yearly profits of a company is \( \$ 25,000 \). The profits have been decreaine by \( 6 \% \) per year. A. Write an exponertial decay function to represert this 8. What will be the profits in 8 years? pound your tituation. avwer to the nearest dollar. Solve the Exponential Equation. 1. Write the following in exponential form: (a) \( \log _{3} x=9 \) (d) \( \log _{4} x=3 \) (b) \( \log _{2} 8=x \) (e) \( \log _{2} y=5 \) (c) \( \log _{3} 27=x \) (f) \( \log _{5} y=2 \) 2. Write the following in logarithm form: (a) \( y=3^{4} \) (d) \( y=3^{5} \) (b) \( 27=3^{x} \) (e) \( 32=x^{5} \) (c) \( m=4^{2} \) (f) \( 64=4^{x} \) 13) \( 16^{n-7}+5=24 \) 14) \( 20^{-6}+6=55 \) 15) \( 5 \cdot 6^{3 \ln }=20 \) 16) \( 8^{-5 x}-5=53 \) 17) \( 3.4 e^{2-2 n}-9=-4 \) 18) \( -6 e^{2 n+8}-3=-23 \) 19) \( -e^{-39 n-1}-1=-3 \) 20) \( -2 e^{7 v+5}-10=-17 \) Expand each logarithm. 1) \( \ln \left(x^{6} y^{3}\right) \) 2) \( \log _{y}\left(x \cdot y \cdot z^{3}\right) \) 3) \( \log _{9}\left(\frac{3^{3}}{7}\right)^{4} \) 4) \( \log _{1}\left(\frac{x^{3}}{y}\right)^{3} \) 5) \( \log _{s}\left(a^{6} b^{5}\right) \) 6) \( \log _{4}\left(6^{3}-11^{3}\right) \) 7) \( \log _{3}\left(\frac{u^{3}}{v}\right)^{2} \) 13) \( \log _{5}\left(\frac{x^{3}}{y}\right)^{n} \) 9) \( \log _{4}\left(3 \cdot 2 \cdot 5^{6}\right) \) 15) \( \log _{2}\left(u \cdot v \cdot w^{2}\right) \) Condense each expression to a single logarithm. 21) \( 2 \log _{6} u-8 \log _{6} v \) 22) \( 8 \log _{5} a+2 \log _{5} b \) 23) \( 8 \log _{3} 12+2 \log _{3} 5 \) 24) \( 3 \log _{4} u-18 \log _{4} v \) 25) \( 2 \log _{5} z+\frac{\log _{5} x}{2} \) 26) \( 6 \log _{2} u-24 \log _{2} v \) 29) \( 3 \log x-5 \log y \) 30) \( 6 \log _{6} 10-24 \log _{5} 3 \) 31) \( \ln z+\frac{\ln x}{3}+\frac{\ln y}{3} \) 32) \( 3 \log _{4} x+9 \log _{4} y \)