1. Warm Up 1. Given the following piecewise function: 1. Evaluate it at f(-4) and f(8) 2. Is it continuous? 2. Given the equations f(x) = 5x 2 and g(x) = 8x – 5, answer the following questions: 1. What is the inverse of g(x)? 2. What is (f + g)(x)? 3. What is (f/g)(3)? 4. What is f(g(x))? 5. What is (f  g)(x)?

2. 1. Given the following piecewise function: 1. Evaluate it at f(-4) and f(8) 2. Is it continuous?

3. 1. Given the equations f(x) = 5x 2 and g(x) = 8x – 5, answer the following questions: 1. What is the inverse of g(x)? 2. What is (f + g)(x)? 3. What is (f/g)(3)? 4. What is f(g(x))? 5. What is (f  g)(x)?

4. QUICK REVIEW OF MODELING AND REGRESSION AND THEN IT’S TRASHKETBALL TIME! Review Day 1: Trashketball Edition

5. Important Topics to know for Midterm Factoring Solving literal equations Evaluate and continuous piecewise functions Logarithms Composition, Operation, and Inverse Functions Vertex, Vertex Form, and Zeroes (Real or Complex?) of Quadratic Equations Linear and Quadratic Regression Parent Functions Transformations Asymptotes Describing a graph (Intervals Increasing and Decreasing, Critical Points, End Behavior, Even vs. Odd degree, Highest Power, Sign of Leading Coefficient)

6. What about the following problem? Larry the taxi driver charges a specific amount per ride. Bobby does not know the exact rate. However, Bobby does know that the rate is linearly related to the number of miles driven. He also knows that when Susie rode in Larry’s taxi, she drove from Charlotte to Atlanta and Larry charged her $490. The distance from Charlotte to Atlanta is 240 miles. Bobby also knows that Larry charged Henry $1310 to travel from Charlotte to New York. The distance from New York to Charlotte is 650 miles.  Write a linear equation that relates the number of miles driven to the price rate.  If Bobby has $1000, does he have enough money to pay for a 500 mile cab ride?

7. Linear Regression The table above shows how far a swimmer has gone after jumping off the starting block during a race. a. Find the linear regression of the data. b. Is it a good fit? How do you know? c. According to this model, how long will it take the swimmer to go 50 meters? d. According to this model, a person who swims for 45 seconds should go how far? Note: You know if a line of best fit is a good fit if the r/r 2 value is close to one, or if your scatterplot in Stat Plot closely matches your line of best fit on the graph.

8. Quadratic Regression The concentration (in milligrams per liter) of a medication in a patient’s blood as time passes is given by the data in the table above. a. Find the quadratic regression equation of the data. b. Is it a good fit? How do you know? c. What will the concentration be after 3 hours? d. When will the concentration in the blood be 0? Note: If a question gives you an “x” value, plug it into your regression equation. If it gives you a “y” value, set Y1 = to your regression equation and Y2 = the given value. Find the intersection! Make sure your window will show you the intersection. If they don’t intersect, it never happens.

9. Trashketball I am splitting you into teams. EVERY PERSON in your group must have a whiteboard and marker. In order for your group to get the chance to shoot, everyone must have all of the correct work and answer on their whiteboard when I count down. When I count down from 5, everyone in your group must silently hold their whiteboards in the air to be eligible. After each round, groups that earn a point for having all of the correct work and answers will earn the right to shoot for more points! The more questions we get through, the better this review is and the more chances your group gets to shoot the ball!

10. Factor x 2 + 6x – 27

11. Solve for m.

12. Draw the Quadratic (f(x) = x 2 ) parent function

13. Based on the graph below, is the piecewise function continuous? Why or why not?

14. Draw the Reciprocal (f(x) = 1/x) parent function

15. Factor 4xy 3 – 6x 2 y 2 – 10x 2 y + 15x 3

16. Draw the Exponential (f(x) = a x ) parent function

17. Evaluate log 8 79

18. Draw the Square Root (f(x) = √x) parent function

19. Solve log 2 (x + 5) + 2log 2 3 = log 2 (4x + 11)

20. Draw the Cubic (f(x) = x 3 ) parent function

21. Given the graph below 1. State the intervals where it is increasing. 2. State the intervals where it is decreasing. 3. Label the critical points and tell whether they are relative or absolute. 4. Use limit notation to describe the end behaviors. 5. What is the highest power in the equation. 6. Is this an even or odd degree function? 7. What is the sign of the leading coefficient?

22. Given the graph below 1. State the intervals where it is increasing. 2. State the intervals where it is decreasing. 3. Label the critical points and tell whether they are relative or absolute. 4. Use limit notation to describe the end behaviors. 5. What is the highest power in the equation. 6. Is this an even or odd degree function? 7. What is the sign of the leading coefficient?

23. What is the asymptote of the graph below?

24. How were the functions below transformed from their parent functions? f(x) = (x – 3) 2 + 5 f(x) = -(x 3 – 1)

25. Factor 6x 2 – 7x – 5

26. Solve log6x = 2