Common Core Math II Study GuideName: ______
Unit 3- Piecewise Functions & Polynomials
- The perimeter of a triangle is represented by the polynomial10x − 1. The length of one side is
3x − 8and the length of a second side is2x − 2. What is the length of the third side?
- What is the AREA of the figure below?
3. What is the area of the figure below?
4. Subtract the polynomials: (7x2 + 5) – (-3x2 – 10).
5. A large rectangle that is 3x + 4 units long and 3x – 4 units wide has a smaller rectangle inside of it that is x + 3 units long and x – 3 units wide. What is the difference in area of the larger rectangle from the smaller rectangle?
6. What ordered pair would represent the y-intercept for the graph of f(x) = -2x3 + 4x2 -3x - 5?
7. Suppose that function f is a 3rd degree polynomial with a lead coefficient of -2. Describe the end behavior of the graph of f(x).
8. Suppose function f(x) is a 2nd degree polynomial and function g(x) is a 5th degree polynomial. Both functions have positive lead coefficients. If an extremely large negative value is substituted in for x, which function will have a larger y-value for the substituted x-value and WHY?
9. Which polynomial has a smaller y-intercept, f(x) = -3x2 -2x – 4 or g(x) = 4x3 +2x – 9?
10. The profit, P, in thousands of dollars, of a company’s product could be represented as P(x) = -(x – 2)(x – 5)(x – 2) where x is the price of the product. Based on the graph of the function, what should the company sell their product for in order to make the most money?
11. A rocket is launched from 200 feet above the ground at time t = 0. The function that models this situation is given by h(t) = – 16t2 + 96t + 200, where t is measured in seconds and h is height above the ground measured in feet. What is the maximum height the rocket will reach?
12. What is the largest x-intercept? Express your answer as a coordinate.
13. What is the value of the y-intercept? Write your answer as a coordinate as well as an equation.
14. Over what intervals is the function decreasing?
15. Over what domain(s) is f(x) > 0?
16. You are looking to purchase t-shirts for your school club. One clothing vendor charges the following prices for t-shirts:
- $20 per shirt for shirt orders up to 20 shirts
- $15 per shirt for shirt orders between 21 and 40 shirts
- $10 per shirt for shirt orders between 41 and 80 shirts
- $5 per shirt for shirt orders over 80 shirts.
Draw a graph to represent the situation.
17. A widget supplier sells widgets at cheaper prices if you purchase more widgets. Below are the prices for different amounts of widgets.
- From 0 to 5 widgets, the price is $10 per widget
- More than 5 and up to 10, the price is $8 per widget
- More than 10 and up to 15, the price is $6 per widget
Draw a graph to represent this situation.
18. What transformations have occurred on the parent function f(x) = |x| in order to have the function g(x) = -|x + 2| - 2?
19. Graph the following piecewise function:
20. Suppose
Find the following:
f(-1) =f(1) =f(4) =