1. Chapter 2 Review
Chapter 2 has taken a long time… you might want to get out your notes and a book to refer to 

2. Section 2-1
Write and equation for the linear function f satisfying the given conditions:
and

3. Section 2-1 Describe how to transform the graph Translate the graph of
2 units left
Vertical Compression by ½
3 units downward

4. Section 2-1
Find the vertex and axis of the graph of the function. Rewrite the function in vertex form (NO CALCULATOR).
Vertex
Axis

5. Section 2-1
Find the vertex and axis of the graph of the function. Rewrite the function in vertex form (NO CALCULATOR).
Vertex (4, 19)
Axis x = 4

6. Section 2-1
Use completing the square to describe the graph of the function. State the vertex, axis and whether the function opens upward or downward
Vertex (2,2)
Axis x = 2
Opens upward

7. Section 2-1
Use completing the square to describe the graph of the function. State the vertex, axis and whether the function opens upward or downward
Vertex (-8, 74)
Axis x = -8
opens downward

8. Section 2-1
Write the equation for the quadratic functions whose graph contains the given vertex and point.
Vertex (1,3) point (0, 5)

9. Section 2-1 Straight-Line Depreciation
Mai Lee bought a computer for her home office and depreciated it over 5 years using straight-line method. If its initial value is $2,350, what is its value 3 years later? (hint: rate of change)
$940.00

10. Section 2-2
Write the statement as a power function equation use k for the constant of variation.
The energy E produced by a nuclear reaction is proportional to the mass m, with constant of variation being

11. Section 2-2
Write a sentence that expresses the relationship in the formula, using the language of variation proportion.
, where n is the refractive index of a
medium, v is the velocity of light in the medium, and c
is the constant velocity of light in free space.
The refraction index n of a medium is inversely proportional to v, the velocity of light in the medium, with constant variation c, the constant velocity in free space.

12. Section 2-2
Diamond Refraction~ Diamonds have the extremely high refraction index of n = 2.42 on average over the range of visible light. Use the formula and the fact m/sec to determine the speed of light through a diamond.
m/sec.

13. Section 2-2
Boyle’s Law ~ The volume of an enclosed gas (at a constant temperature) varies inversely as the pressure. If the pressure of a 3.46-L sample of neon gas at is atm, what would the volume be at a pressure of atm if the temperature doesn’t change. L

14. Section 2-3
Graph the function in a viewing window that shows all if its extrema and x – intercepts. Describe the end behavior.

15. Section 2-3
Graph the function in a viewing window that shows all if its extrema and x – intercepts. Describe the end behavior.

16. Section 2-3
Find the zeros of the function algebraically
and

17. Section 2-3
Find the zeros of the function algebraically
, and

18. Section 2-3
Using only algebra, find the cubic function with the given zeros. 3, -4, 6

19. Section 2-3
Use cubic regression to fit a curve through the four points given in the table x Y

20. Section 2-3 Stopping distance at 25 mph approx. 56.39 ft.
A state highway patrol safety division collected the data on stopping distance in table 2.14.
Find the quadratic regression model
Use the regression model to predict the stopping distance for a vehicle traveling 25 mph.
Use the regression model to predict the speed of the car if the stopping distance is 300 ft.
Stopping distance at 25 mph approx ft.
Speed with a stopping distance of 300 ft mph

21. Section 2-4
Divide f (x) by d (x) write the summary statement polynomial form and fraction form.

22. Section 2-4
Divide using synthetic division, write a summary statement in fraction form.

23. Section 2-4
Divide using synthetic division, write a summary statement in fraction form.

24. Section 2-4
Find the polynomial function with leading coefficient 2 that has the given degree and zeros
-2, 1, 4

25. Section 2-4
Use synthetic division to prove that the number k is an upper bound for the real zeros of the function f.
Yes all the numbers in the last line are , 3 is an upper bound

26. Section 2-4
Find all the possible real zeros of the function, use exact values.
Rational zeros -3; irrational

27. Section 2-5
Write the polynomial in standard form, and identify the zeros of the function and the x- intercepts of the graph.
zeros ; x – intercepts: none.

28. Section 2-5 State how many complex zeros the function has.
2 complex; no real

29. Section 2-5
Find all the zeros and write a linear factorization of the function.
Zeros: -1, 1,

30. Section 2-6
Find the domain of the function f. Use limits to describe the behavior of f at value(s) not in its domain. No calculator.
Domain:

31. Section 2-6 Find the horizontal and vertical asymptotes of
f (x). Use limits to describe the corresponding
behavior. No calculator.
Horizontal: 0, Vertical 0, 1

32. Section 2-6
Find the asymptotes and intercepts of the function No Calculator
Intercepts: and
Vertical asymptotes: x = -1, 3
Horizontal asymptotes: y = 0

33. Section 2-6
Find the intercepts, asymptotes, use limits to describe behavior at the vertical asymptotes and analyze the function:

34. x intercept: (1,0) y intercept: (0,1/12)
VA: x = -3, 4 HA: y = 0
Domain: Range:
Continuity: Decreasing:
Not Symmetric, unbounded No local extrema
End behavior:

35. Section 2-7
Solve the equation algebraically check for extraneous solutions.
x = -4 or x = 3, but 3 is extraneous

36. Section 2-7
Solve the equation algebraically, check for extraneous solutions.
x = 5 or x = 4

37. Section 2-7
Solve the equation algebraically. Check for extraneous solutions.
x = 5 or x = 0, 0 is extraneous

38. Section 2-7
Solve the equation algebraically
No real solutions

39. Section 2-7
Acid Mixture ~ suppose that x mL of pure acid are added to 100 mL of a 35% acid solution.
a) Express the concentration C (x) as a function of x.
b) Determine how much pure acid should be added to
35% solution to produce a new solution that is 75%
acid.
160 mL

40. Section 2-8
Determine the x values that cause the polynomial to be (a) zero (b) positive (c) negative.
(a) when x = -7, -4, 6
(b) when
(c) when

41. Section 2-8 Solve the inequality for the given f (x) (a) (b) (c) (d)
(a) both factors, so f (x) is always positive
(b) for same reason as (a)
(c) no solution – never negative
(d) no solution – never negative

42. Section 2-8