Question 3 12 pts 1 0 Details The graph below represents the relationship between the height of a ball and the distance it traveled after the ball was thrown. Ball Throw 20 18 16 14 12 Height (feet) 10 12 16 20 24 28 36 40 44 48 X Distance (yards) Worth 3 points each a) Evaluate f(0). Include units on your paper. f(0) = b) Use the graph to solve f(x) = 8 . Include units on your paper. r = c) When does the ball reach its highest point? What is its maximum height? Write your answer with function notation. d) Select the best description of height of the ball as a function of time: Decreases the entire time Decreases then increases Maintains a constant value Increases the entire time Increases then decreasesQuestion 2 10 pts 01 0 Details Find the value of c, if 2 7 = 9 Show algebraically. Write the answer in decimal form (round to 4 decimal places). Show all work on your notebook paper.Question 4 12 pts 01 0 Details Find all solutions, showing all work: 3a* + 80 = - a-+ 3 a) Give the exact solutions in simplest form Worth 9 points b) Give the solutions rounded to two decimal places. Show work. Worth 3 points. Question 5 8 pts 01 0 Details Factor the following. Write your answers in completely factored form 72a b - 24a b + 2a-b (Worth 8 points)Question 6 12 pts 01 0 Details Find the domain of the following functions, and express your answer with correct notation. This question must be manually checked by instructor. Worth 4 points each a) f(a) = va -7 b) f(a) a+3 a - 3 () y = 7a" + 3a + 2Question 7 12 pts 01 0 Details The width of a rectangle is 2 feet less than the length. Worth 6 points each a) Express the area (A) of the rectangle as a function of its length (L) using correct function notation. Show all work on your notebook paper. b) Use that function to determine the length and width if the area is 120 square feet. Show all your work on your own notebook paper. Please write units on your answers on your paper. Length = Width = . Question 8 12 pts 01 0 Details a) Find the intercepts of the line with equation 3x + 2y = - 6 . Report the intercepts in ordered pair form. (Show work) Worth 6 points each x-intercept y-intercept b) Find the distance between those two intercepts. Show work and report the simplified exact answer (do not round).Question 9 12 pts 1 0 Details Simplify the following expressions. Assume variables represent positive numbers. Show all work on your notebook paper. a.) 4y' V321 + 4x /8ry b.) ( VI + V7) (VI - V7) = Question 10 16 pts 0 1 0 Details Consider the equation: y = 5x* + 50r + 122 a) Use the modified technique of completing the square to write the equation in vertex form. Work must be shown. Answers without some work will not earn full credit. Manual grading needed Worth 8 points f(x) = b) Report the vertex as an ordered pair Worth 2 points c) Find the x-intercepts. Give exact answers. Worth 4 pointsQuestion 11 @ 10 pts 1 0 Details For the function defined by f(x) = -x + x , find the average rate of change from r = - 3 to r = 0 . Show all your work on your notebook paper. Worth 10 points Question 12 15 pts 0 1 0 Details In baseball, the flight of a pop-up may be described as d = - 16t' + 80t + 3.5 where d gives the ball's height above the ground in feet after t seconds. Worth 5 points each a) How long after the ball is hit, is it 50 feet from the ground? Round your answer to nearest 0.1, if needed. Show all work on your notebook paper and include units on your paper also. b) What is the maximum height reached by the ball? Round your answer to nearest 0.1, if needed. Show all work on your notebook paper and include units on your paper also. c) How long after it is hit will it touch the ground? Round your answer to nearest 0.1, if needed. Include units in your answer.Question 13 12 pts 01 0 Details a. Find the value of x, if log, * = 3 Show all work on your notebook paper. b. Find the value of r, if logs = 3 Show all work on your notebook paper. Question 14 8 pts 01 0 Details Simplify (worth 8 points) 2 + x3 - 7x + 12 - 4Question 15 14 pts 1 0 Details The value of painting made by a famous artist was $2,830 in 2010 and $4,207 in 2019. (worth 5 points) a. Find a formula linear function that models the values of the painting, V, t years since 2000. (Note: t = 0 is the year 2000.) Show all steps on your notebook paper. Write answer in function notation. (worth 3 points) b. Use the model from part (a) to determine the value of the painting in the year 2030. Show all steps on your notebook paper. State your answer using a complete sentence in the box below, including units if applicable. (worth 4 points) c. Use the model from part (a) to predict how many years it takes for the painting's value to reach $4,819. Show all steps on your notebook paper. State your answer using a complete sentence in the box below, including units if applicable.Question 16 15 pts 01 0 Details An investor deposits $9000 in a retirement account that returns 3.1% at the end of each year. Worth 6 points a) Write a function that models the amount of money, A , in the account at the end of y years. (must use y for years) A(y)= Worth 4 points b) Use that model to find the amount of money after 8 years. Round to the nearest cent. Worth 5 points c) Use that function to determine when the account will reach $16000, assuming a constant interest rate. Round your final answer to nearest year, if needed.Question 17 12 pts 01 0 Details Write each in simplest form. Showing work. Need manual grading. Worth 6 points each Part a 4y 14 -10 Part b y yQuestion 18 8 pts 01 0 Det This question has two parts. This question has to be manually graded Worth 4 points each Part a: Draw a graph that represents a function. -7 -6 -5 5 -4 -3 -2 -1 1 2 3 4 5 6 7 Clear All Draw: Part b: Draw a graph that represents a NON-function -7 -6 -5 -4-3 -2 1 2 3 4 5 6 7 Clear All Draw