Finish every page

1.1: Problem Set Overview In this assignment you will be completing problems based on the parent functions we have learned in this topic. The purpose of this assignment is to identify the key features of the given function using knowledge of their parent functions . Problem Sets Questions Rewrite the Functions to identify the key features specied for each and graph if asked. 1. Rewrite 3x + 4y 2 8 in slope intercept form and identify the slope, y- intercept, end behavior and graph. Slope-intercept Form: Show work here: Slope: y-intercept: End Behavior: Graph: 2. Rewrite f(x) = x - 6x + 5 in vertex form and find the vertex, max/min, increase/decrease intervals, range, end behavior and graph. Vertex Form: Vertex: Show work here: Max/Min:_ Increase/Decrease Intervals: Range End Behavior: Graph:3. Rewrite f(x) =- 2x" + 4x + 2 in vertex form and find the vertex, max/min, increase/decrease intervals, range, end behavior and graph. Vertex Form: Vertex: Show work here: Max/Min:_ Increase/Decrease Intervals: Range: End Behavior: Graph: 4. Rewrite f(x) = 2x - 8x - 10 in factored form to find the x intercepts and sketch. Factored Form:. X intercepts:5. A soccer ball kicked off the ground has height modeled by the function h(t) = 61k3 + 6t, wheret is the number of seconds since the ball was kicked and h is the height in meters. What is the maximum height reached by the ball? 2.3 Assignment 2: Problem Set Overview In this assignment you will be completing problems based on graphing and modeling polynomial functions. The purpose of this assignment is to practice graphing and modeling polynomial functions. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. A third degree polynomial function f has real zeros -2, 2, and 3, and its leading coefficient is negative Write an equation for f. Sketch the graph of f. How many different polynomial function are possible for f? 2. Write the polynomial and sketch the graph of a fifth degree polynomial function whose leading coefficient is positive 1 and has zeros of 4 multiplicity 2 and 0 multiplicity 33. The graph of one of the following functions is shown below. Identify the function shown in the graph and explain why the other is not the correct function. a. y = x (x + 2)(x - 3 b. y = x(x+ 2)(x - 3)\fUse the following table to answer questions 4 and 5. Interval Value of f (x) (- 00, - 2) Positive (- 2, 1) Negative (1, 4) Negative (4, 00) Positive 4. What are three real zeros of the polynomial function f? 5. Can the degree of f ever be odd? Explain?2.5 Assignment 2: Problem Set Overview In this assignment you will be completing problems based on graphing rational functions. The purpose of this assignment is to practice graphing rational functions and matching rational functions with their equations based on key features of rational functions. . As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. Find the intercepts of the function, then sketch a graph of the function. 2. Find the asymptotes and intercepts of the function, then sketch the function. x '2 '2 . _ x '33' 3 3. What is one possible equation for the following function? -8 -7 -6 -5 -4 -2 -1 -N 3 4 5 64. Identify one possible equation for the graph below. Notice the table of values given for the graph. 5 x f(x) -3 -2 4 2 0 0 undefined 2 2 -2 3 0 5. The function of g (x) = - has been transformed to produce the image h(x) = -. Describe the transformations that occurred. Then sketch both graphs on the same coordinate plane3.1: Problem Set Overview In this assignment you will be completing problems based on the graphs of exponential and log functions. The purpose of this assignment is to familiarize with recognizing and graphing exponential and log functions. .As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. Sketch the graph of the following function by rst making a table of values when x = -2, -1, -, 1, and 2. You may use a calculator to help you approximate the answers. y=3 2. For each of the following functions, identify if it is an exponential function. If it is, give the initial value and base number. 3. Write an equation for the exponential function with the given values below: 3 l 1 2 E 1 1 l v \f5. The graph of the exponential function y = log2(x + 3) + 1 is graphed below. Write an equation for the inverse function and sketch the graph of its inverse. 3.2: Problem Set Overview In this assignment you will be completing problems based on solving log and exponential equations. . The purpose of this assignment is to use logarithmic properties to solve equations. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. Rewrite as an exponent and then evaluate: logzx = 3. Z 2. Write logfa as an expression in terms of log a, log 0, and log a. 3. Solve log(x+15)+log(x+1)=0.5log4+log3+log(3x+5) 4. Rewrite as a logarithm to solve 5" = 2. Round your answer to three decimal places. 5.Solve 4In(3x+1)=2. Express your answer exactly using e and then as a decimal rounded to three decimal places.3.3 Assignment 2: Problem Set Overview In this assignment you will be completing problems based on solving exponential and logarithmic equations. The purpose of this assignment is to practice solving exponential and logarithmic equations. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below using properties of log and exponential functions. Show your work. 1. log, (3x + 1) =- 4 2. Solve for x: In(4x) + In(3) - In(2) = 43. Find the solution by graphing: X - 3 = log (x + 1) 4. In(3x-2)+In(x-1)=2Inx\fTopic 14 Assignment 2: Problem Set Overview In this assignment you will be completing problems based on angles, radians and arc length. The purpose of this assignment is to convert angle measures from radians to degrees and from degrees to radians. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. Convert: 85 degrees to radians 21 to degrees 2. Find the radian measure of a central angle that intercepts an arc of length I in a circle of radius r.3. Use the arc length formula to find the missing information in the table below: r ? 2 in 25 rad 1.5 ft ? "rad 5ft 18 degrees 4. A circle has a radius of 7 units and has a sector formed by a central angle of 40 degrees. Find the arc length and area of the sector. Round to the nearest tenth.5. On a new vehicle, a windshield wiper is 50 cm long and is affixed to a swing arm that is 74 cm long from pivot point to wiper-blade tip. If the swing arm turns through 110 degrees, what area of the windshield is swept by the wiper blade?1.2: Problem Set Overview In this assignment you will be completing problems based on composition of functions. The purpose of this assignment is to perform operations with functions and create compositions of fucntions. Problem Sets Questions Solve the questions below. Show your work. 1. Use the functions below to perform the operations indicated: f(x):2x5 g(x):2x23x5 h(x):x3+6x1 2. Use the functions below to perform the operations indicated: f(x):2x5 g(x):2x23x5 h(x):x3+6x1 a) (h g)(x) b) (ghXO) 3. Use the functions below to perform the operations indicated: f(x):2x5 g(x):2x23x5 h(x):x3+6x1 a) (h 9)(* 1) b) (3 DOC) 4. Use the graphs below to perform the operations indicated. f(x) is the blue graph, g(x) is the red graph and h(x) is the green graph. a) (f + g)( 1) b) (g MU) 5. Use the graphs below to perform the operations indicated. f(x) is the blue graph, g(x) is the red graph and h(x) is the green graph. a) 0! ( 1) b) (fg)( 2) 1.3: Problem Set Overview In this assignment you will be completing problems based on modeling parent functions. The purpose of this assignment is to practice modeling functions based on real world scenarios. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. The cost of a cell phone service can be modeled by the equation C(m) = 5m + 23. 42 where C(m) is the total cost for m minutes of cell phone use. State the meaning of the slope and y-intercept of this function with respect to the costs associated with the cell phone service. 2. Using the parent function y = 3", write the equation of an exponential function that is flipped over the X-axis, shifted 3 to the right and 4 down.Z 3. The graph of a parent function is shown below. Sketch the graph of the transformed function if the new image is represented by the function f(x) : xl'x + 2. 4. The number of cars C a car dealer sells in each month of the year from January to October can be modeled by the function B = 15|t 5| + 100 where t is thetime in months and t = 1 represents January. What is the maximum number of sales in one month? In what month is the maximum reached? 5. A city's population has been recorded over a period of ten years. The data shows a constant growth between each year. Which function type would you use to model this situation? Explain why the function type you chose is the best option.2.2: Problem Set Overview In this assignment you will be completing problems based on finding real and complex zeros of polynomials. The purpose of this assignment is to practice using different methods to find real and complex zeros of polynomials. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. 1. Sketch a graph of the following polynomial. Show all x-intercepts. y: -2(.\\- + 3)(.\\' 0.5)(.\\' + 1) 5 2. Given that 2 i + 2 is a zero off(x) = x , 6x4 + 11x3 2 x2 , 14x + 5, find all complex roots using 3 nthetic division. List our ossible rational roots also. 3. Determine k so that f (x) = x - 11x + kx - 4 has x - 2 as a factor. 4. True or False. If False, explain why or provide a counterexample A polynomial of the 5th degree can have only 2 real roots and 3 imaginary roots 5. A polynomial P(x) has the following roots: - 2, 1 + 3i, 5i. Write an equation of the function of lowest possible degree and use that to find the particular equation if P(0) = 25.3.4: Problem Set Overview In this assignment you will be completing problems based on using exponential and logarithmic functions to model situations. The purpose of this assignment is to use logarithmic and exponential functions to model situations. As you work, show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. The following situation will be used for Questions 1-3. Suppose a culture of 1000 bacteria is put into a petri dish and the culture triples every hour. Predict when the number of bacteria will reach 250,000. 1. Use the given information to write the exponential equation used to model this situation. Identify the variables used. 2. Use log properties to solve the equation you developed in question 1.3. Use a graphing calculator to check your work. Describe how the graph of the exponential equation can help you solve the equation and/or check your answer. What are you looking for on the graph? Is your answer correct? The following will be used for questions 4 and 5. A virus is spreading in a local school. The virus is spreading logistically so that it follow the below model: P(t) = 1200/(1 + 39e . tis the number of days since the start of the virus. P(t) represents the number of people infected on day t. 4. How many people are infected by the end of Day 0? 5. How long does it take for 1000 people to become infected?Topic 13 Assignment 2: Problem Set Overview In this assignment you will be completing problems based on right triangle trigonometry and special right triangles. The purpose ofthis assignment is to use trigonometry to find unknown side lengths and angle measures in right triangles. As you work, show your thinking in the box below. Draw diagrams to help get started. Problem Sets Questions Solve the questions below. Show your work. 1. Atree casts a shadow that is 23 ft long. The angle of elevation of the sun is 45 degrees. What is the heioht of the tree? 2. You are flying a kite and have used 24 ft of string but it got caught in a 13 ft tree. What is the angle of elevation to the location of the kite? 3. A group of kids made a ramp for their skateboards. The ramp is 19 feet long. If the horizontal distance of the ramp is 15 ft, what is the vertical distance? 4. The shortest side of a 30-60-90 triangle is 20. Find the lengths of the other sides. 5. A square ABCD has a diagonal length of 1112. Find the square's perimeter and area\f4.: Problem Set Overview In this assignment you will be completing problems based on the unit circle. The purpose of this assignment is to evaluate trigonometric functions using the unit circle. As you work, have the unit circle resource sheet in front of you and show your thinking in the box below. Problem Sets Questions Solve the questions below. Show your work. Use these directions for questions 1-3. For each given point P located on the unit circle, state the quadrant and find sine, c053 and tan 8. 1. 13('71, g) 2. P(0, 1) 3- 13(32 i) 2 ' 2 4. Find the exact value of cos 600 decrees . 231T 5. Find the exact value COST 82 Assignment 2: 3 Reads Strategy Problem Set Overview In this assignment you will be completing problems based on the 3 reads method of problem solving. The purpose of this assignment is to demonstrate your ability to solve and analyze problems using this method. As you work, refer to the Video lesson as needed, and do your best! Problem Sets Questions Solve the questions below. Show your work. 1. Use the following problem to complete the first two parts of the 3 reads strategy and answer the following questions. 0 What is the context of the problem/ What is it asking? o What are the important quantities in the problem? 0 What are the math action words? What operations would you use? Maxine is growing a rectangular garden. She wants the total area of her garden to be 32 square feet. If the length of her garden is 4 feet less than the width, what are the dimensions of her garden? 2. Using the same problem as the previous question, complete the 3 reads strategy by solving the problem. Show your work and answer the following questions. 0 Did you answer the task completely? 0 Is your answer reasonable? Maxine is growing a rectangular garden. She wants the total area of her garden to be 32 square feet. If the len th of her arden is 4 feet less than the width, what are the dimensions of her arden? 3. The students in the Hawkins High physics class are doing an experiment. They are throwing items from the second story balcony to see how far away the item lands. One student throws his lunch box over. The path the lunchbox takes can be modeled by the following function: f(t)=-16t2+79t+5, where t represents the amount of time the item is in the air. How long is the lunch box in the air? Use the three reads method to solve this problem. 4. Solve the following problem using the 3reads method. A movie theater sold 180 more adult tickets than child tickets. Adult tickets cost $12.50 each and child tickets cost $7.50 each. What is the minimum type of ticket sold so that the total amount sold is at least $4500? 5. In 3 years, the sum of Adam's and Briana's ages will be 46. Adam is now 7 years more than ten times Briana's age. How old is Adam now? How old is Briana