1. MATH 110 Review EXAM 2

2. Jeopardy Old & New CombosLinesQuads Poly Want a Cracker Potpourri 100 200 300 400 500

3. Potpourri 100 Explain whether or not the table below represents a linear function: Answer: no; the rate of change is not constant. X12345 Y3.05.17.29.311.5

4. Potpourri 200 Consider the polynomial function What is the degree of P(x)? State the end behavior of P(x) State the multiplicity of each zero Answer: degree 6 ; y →-∞ as x →±∞; -2 has multiplicity of 3, 4 has multiplicity of 2, and -5 has multiplicity of 1.

5. Potpourri 300 An airplane flies at 80 mph for the first third of a trip and then 120 mph for the rest of the trip. The entire trip is 400 miles. How long does the trip take? Answer: 3.75 hours

6. Potpourri 400 A restaurant’s profit P as a function of the number of meals served m is given by the equation State the intercepts and give a practical interpretation for each. What is the slope of this line? What does this number tell you about the profit? Answer: y-int (0,-200) means profit is -200 dollars; x-int (60,0) break-even point ; slope is (10/3) meaning every three meals served, the profit increases by 10 dollars.

7. Potpourri 500 A horticulturist has determined that the number of inches a young redwood tree grows in one year is a function of the annual rainfall r given by : What is the maximum number of inches a redwood can grow in one year? Answer: 13.5 inches.

8. Poly Want A Cracker 100 What is the smallest degree the polynomial could have? What is the sign of the leading coefficient? Answer: minimum degree 5 ; lead coefficient positive

9. Poly Want A Cracker 200 Find the equation of a polynomial function with the following information: 1.Negative lead coefficient 2.Even degree 3.Zeros at -3 (multiplicity 1), 0 (multiplicity 1), and 5 (multiplicity 2) Answer: y = -x(x+3)(x-5) 2

10. Poly Want A Cracker 300 What is the remainder for the following division: Answer: -x+15

11. Poly Want a Cracker 400 Consider the polynomial function Which of the following is/are true? 1.-2 is a zero of f(x) 2.x – 2 is a factor of f(x) 3.f(x) has only one real zero

12. Poly Want a Cracker 500 Solve the polynomial equation given below: Answer:

13. Quads 100 Find the equation of a quadratic with vertex (2,-1) and passing through the point (1,3). Answer:

14. Quads 200 Rewrite the quadratic function given in standard form: Answer:

15. Quads 300 Find the vertex and intercepts of the quadratic function given: Answer: V(-0.1,0.03) ; intercepts: (- 0.647,0), (0.447,0) and (0, 29/1000)

16. Quads 400 A box is being constructed by cutting 2 inch squares from the corners of a rectangular piece of cardboard that is 6 inches longer than it is wide. If the volume of the box is to be 224 cubic inches, find the dimensions of the cardboard. Answer: 12 inches by 18 inches

17. Quads 500 A frame for a picture is 2 inches wide all around. The picture inside the frame is 4 inches longer than it is wide. If the area of the picture is to be 320 square inches, find the outside dimensions of the picture frame. Answer: 20 inches by 24 inches.

18. Lines 100 Write the equation of the line passing through (-2,2) and having a slope of -0.5. Answer: y = -0.5x+1

19. Lines 200 Write the equation of the line containing the points (2,3) and (5,15) Answer: y = 4x-5

20. Lines 300 Fill in the table below so that the function is linear: Answer: the missing y values in order are 4 and 0.25. The missing x values in order are 2 and 4.08. x 01.53 f(x)6.5-3.5-6.2

21. Lines 400 Find k so that the line containing the points (-3,k) and (4,8) is parallel to the line containing the points (5,3) and (1,6). Answer: k = 13.25

22. Lines 500 On most state highways, the fine for speeding depends on the speed of the car. In a certain state where the speed limit is 65 mph, the fine for driving 70 mph is $30 and the fine for driving 85 mph is $90. Assuming this relationship is linear, find the equation of the line that expresses the fine as a function of the speed of the car. How fast do you need to be driving to be fined $110? Answer: Equation: y = 4x-250 ; 90 mph

23. Combos 100 Given the functions and State the domain of (f + g)(x) Answer: [4,∞)

24. Combos 200 Consider the functions and State the domain of (f/g)(x) Answer: (-2,0) U (2,0)

25. Combos 300 Consider the functions and Find Answer:

26. Combos 400 An accident at an oil drilling platform is causing a circular shaped oil slick to form. The volume of the slick is roughly given by where r is the radius of the slick in feet. At the same time, the radius of the slick increases according to the function where t is in minutes. Find V(r(t)) and give a practical interpretation How long until the volume of the slick is 226 cubic feet. Answer: V(r(t)) tells us the volume of the slick t minutes after it started. It takes about an hour for the slick to reach 226 cubic feet.

27. Combos 500 Find f(g(2)) and g(f(0)) given the tables below: Answer: 3 ; 1 xf(x)g(x) 022 132 211

28. Old & New 100 Given that (3,4) is a point on the graph of f(x), which of the following must a point on the graph of a)(-6, 2) b)(-6, 8) c)(-1.5, 2) d)(-1.5, 8)

29. Old & New 200 Write the equation of the base graph which has been transformed in the following ways: first, reflected over the x- axis, vertically compressed by one-third, shifted right 4 units. Answer:

30. Old & New 300 Consider the function. What is the equation of the graph that will compress the graph horizontally by a factor of 3, move the graph left 2 units and reflect the graph over the x-axis (in that order). Answer:

31. Old & New 400 Suppose that a function f(x) has a domain of [-6,4]. What will the domain be for the function ? Answer: [-16,14]

32. Old & New 500 Suppose that a function f(x) has a range of [-2,1]. What will the range be for the function ? Answer: [3,9]