Unit 1 Post-Test NAME: ______DATE: ______Period : ______
Modeling Functions
ReTest
SCORE:
Solve a system of equations Graph linear, absolute value, and quadratic functions
Solve a system of inequalities Write linear, absolute value, and quadratic functions
Solve for a specific variable Evaluate and apply various functions
ALGEBRA: ______/ ______= ______% FUNCTIONS: ______/ ______= ______%
ALGEBRA
1. You have 10 fewer quarters than dimes and 5 fewer nickels than quarters. The total value
of the coins is $4.75. How many quarters, nickels, and dimes do you have?
2. Solve for y:
3. A fruit market is selling oranges in a 5 lb bag for $6 and a 10 lb bag for $10. You spend $68 and buy a total of 8 bags of oranges. How many 5 lb bags and 10 lb bags of oranges did you buy? How many total pounds of oranges did you buy?
4. Solve the system:
5. An office building containing 96,000 square feet of space is to be made into apartments. There will be at most 15 one-bedroom units, each with 800 square feet of space. The remaining units, each with 1200 square feet of space, will have two bedrooms. Rent for each one-bedroom will be $650, and for each two-bedroom unit it will be $900. Let x represent the number of one-bedroom units and y represent the number of two-bedroom units.
a. Write a system of inequalities to represent the situation.
b. Graph the system of inequalities and Label your vertices.
c. Find the number of each type of apartment that maximize profit.
FUNCTIONS
YEAR / 2005 / 2006 / 2007 / 2008 / 2009Households with P.C.s (millions) / 53.2 / 58.7 / 64 / 67.8 / 71.9
6. Represent the data using each of the following:
a. a mapping diagram b. ordered pairs c. graph on coordinate plane
7. Write a function to model the cost of renting a truck for one day. Then evaluate the function for the given number of miles.
Daily rental: $19.95
Rate per mile: $.30 per mile
Miles traveled: 75 miles
8. Evaluate the function for the given value of x, and write the input x and the output f (x) as an ordered pair.
a. f(x) = ½ x – 18 for x = ¼ b. Find the Error: Evaluate f(x) = 3x2 – 4x + 1 for x = -5
f( -5) = 3(-5)2 – 4(5) + 1
f( -5) = 3(25) – 4(5) + 1
f( -5) = 56
9. Given (8, -3) and (-4, 5) find the following:
a. Calculate the slope between the points
b. Write the equation of the line passing through those points
c. Write the equation of the line parallel to the one you found in part (b) passing through (6, 1)
d. Write the equation of the line perpendicular to the one you found in part (b) passing through (6, 1)
e. Graph the equation of the line you found in part (b).
10. In a newspaper poll taken before an election, 53% of people favor the incumbent mayor. The margin of error for the actual percentage, p, is less than 5%.
a. Write an absolute value inequality that represents this situation.
b. Solve. State the meaning of the answer in the context of the problem.
11. Write the function represented in each graph. Then state the domain and range of each.
a. b. c.
12. Use the function, f(x) = –4 │x – 1│+ 2 answer the following:
a. Graph the function (label the vertex)
b. State the transformations to the parent graph
c. State the domain and range of the function
13. Use the function, f(x) = x2 + 4x – 7 answer the following:
a. Graph the function (label the vertex, axis of symmetry, and y-intercept)
b. Write the function in vertex form
c. State the transformations to the parent graph
d. State the domain and range of the function
14. A player hits a tennis ball across the court and records the height of the ball at different times, as shown in the table.
a. Find a quadratic model for the data.
b. Use the model to estimate the height of the ball at 4 seconds.
c. What is the ball’s maximum height?
15. A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P = -0.03n2 +1.80n - 10. P is the profit in thousands of dollars and n is in thousands of units.
a. How many DVDs should the company produce to maximize the profit?
b. What will the maximize profit be?
Performance Tasks:
ALGEBRA
16. Given the inequality │x + 2│ ≥ k , find a value of k, if possible, that satisfies each condition. In each case, explain your choice.
a. Find a value of k such that the inequality has all solutions.
b. Find a value of k such that the inequality has exactly one solution.
c. Find a value of k (different from your value in part b) for which a solution exists but for which the solution set does not include 5.
FUNCTIONS
17. Write a short paragraph about the similarities and differences of the types of functions covered in this unit (linear, absolute value, quadratic). Reference which functions are even and which are odd and justify your choice. Be sure to thoroughly answer in vivid detail.
(BONUS) Given the data below: Find the recursive and explicit equations: