Please have each project separated.

Math 120 - Unit 2 Project C The directions for this assignment are inside the course. 1) Describe the transformations that would produce the graphs from the graph of f (x) = x. Be specific and detailed. If more than one transformation is needed, specify the order in which the transformations should be applied. a. y = f(3x) +5 b. y= -f(x+2)-6 2) The graph of f(x)=vx is shifted to the right 3 units, reflected across the x-axis, and stretched vertically by a factor of 4. Write the new function g(x) = ory =. 3) f (x) = 2x-+ 3x -5 a. For the polynomial above, find the zeros algebraically and the multiplicity for each. Be sure to show all work. b. Use a graphing utility (desmos.com) to graph the polynomial. Show your graph on your paper. c. How do the zeros from part a relate to the graph from part b? 4) g(x) =4x - 8x- - 11x - 3 d. For the polynomial above, find the zeros algebraically and the multiplicity for each. Be sure to show all work. e. Use a graphing utility (desmos.com) to graph the polynomial. Show your graph on your paper. f. How do the zeros from part a relate to the graph from part b? How does the multiplicity for each zero relate to the graph?Math 120 - Unit 3 Project C The directions for this assignment are inside the course. 1) Suppose you are a microbiologist studying a type of bacteria. The growth of this type of bacteria can be exponentially modeled with the equation y = 5000go where y represents the number of bacterial cells present at any time : (in minutes). a. What does the number 5000 represent in this model? b. How many minutes will it take to reach 300,000 bacterial cells? Round to the nearest minute. 2) A video game released in the year 2001 sold quickly at first, but then sales slowed as time moved on. The number of games sold y (in thousands) are given by the logarithmic model y = 324 + 14.2in x, where x = 1 is the year 2001 a. How many DVDs were sold in the year 2001? How does that relate to the logarithmic equation? b. In what year were 360,000 DVDs sold? 3) Set up, but do not solve, a system of equations for the following application: How many liters of a 36% saline solution and how many liters of a 52% saline solution should be mixed to obtain 125 liters of a 45% saline solution? 4) Solve the system of equations algebraically using substitution or addition elimination: V=x - 6x+ 3 2x + y = 8