Math 1 Study Guide 2015 Name ___________________________________ Per _____

Math 1 Study Guide
Semester 1 Final
Simplify.
1. 2o
2015
Name ___________________________________ Per _____
2. 2-2
3. 22
Evaluate when a = -3 and b = -2.
4. -2a + 5b
5. 6a – b
6.
7.
8.
9.
What is the constant difference? _______
What is f(0)? __________
What is the explicit equation?_____________________
What is the recursive equation (don’t forget f(0))
_________________________________________
10.
11.
12.
13.
What is the common ratio? ______
What is f(0)?
_______
What is the explicit equation? __________________
What is the recursive equation (don’t forget f(0))
_________________________________________
x
f(x)
1
6
2
3
3
0
4
-3
x
f(x)
1
100
2
50
3
25
4
12.5
14. Write the recursive equation for f(x) = 4 + 2x.___________________________________________
15. Write the explicit for f(0) = 3; f(x) = f(x – 1) ∙ 5.
_____________________________________
16. Write the explicit equation for f(0) = -2, f(x) = f(x – 1) – 5
17. Write the recursive equation for f(x) = 2 ∙ (3)x
_____________________________________
____________________________________________
18. If f(0) = 4, write the explicit equation you would use to find the next term if it was increasing by 15%?
______________________________________
19. Find the common ratio.
_____________
x
f(x)
1
5247
2
6296.4
3
7555.68
4
9066.816
20. Which type of function always travels at the same rate? ______________________________
21. Which type of function may start out slow, but then its increase becomes greater and greater?
______________________
22. If there are 25,682 people living in Jarvieville in 2015, and the population increases 20% each year….
a) write the equation to use to predict future years. ______________________________
b) How many people will there be in this town in the year 2018? ____________________
Determine whether the equations are linear (L) , exponential (E) or neither (N).
23. y = 4x – 2
24. y = x2
25. y = 6x
26. f(x) = 3f(x – 1)
27. f(x) = 4∙(3)x
28. f(x) = f(x – 1) – 3
Find the slope and y-intercept of the following equations. Write the y-intercept as an ordered pair.
29. y = 3x + 2
30. y = 4 – x
31. f(x) = 1/5x
32. f(x) = –2x – 1/3
33. If the slope is (-5) and the y-intercept is 3, write the equation in slope-intercept form. _______________________
Graph the following functions.
34. y = 3 – 1/2x
35. f(x) = 2x – 4
36. f(x) = 2x
37. y = 2 ∙ 3x
38. Sketch a graph that is NOT a function. Why is your graph NOT a function? _________________________________
_________________________________________________________________________________________________
39. In y = -3x + 5, find f(-3). ____________
40. In y = 3 ∙ (2)x, find f(3). ________________
41. In f(x) = 6 – 2x, find f(8). __________
42. In f(x) = 4x, find f(-2). _________________
43. Graph 2x + 3y = 6.
45. Solve by graphing:
What is the solution? __________
44. Draw any line that has a y-intercept of 3?
Identify the zero term, the f(0).
46. y = -2x + 5
47. f(x) = 7 ∙ 4x
48. What is the slope of y – 4 = 2(x + 5)? ____________
Solve the following equations.
49. 3(x – 3) = 4(x + 8)
50. 6 – 2(x – 4) = 8 – x
51. 6x + 5 = 2x – 19
52.
Arithmetic
256
4
53.
Geometric
256
4
For #54 – 58, use the graph below.
54. What is the maximum? _____________
55. What is the minimum? ______________
56. What is the domain? ___________________________________
57. What is the range? _____________________________________
58. Using interval notation, what interval is increasing?
__________________________________________________
59. How do you write “all real numbers” in interval form? _______________________________________________
60. Write -5 ≤ x < 9 in interval form. _________________________________________
61. What is the slope of a horizontal line? ______________________
62. Find the slope of a line that contains (-3, 2) and (5, 4). _________________
63. Find the slope of a line that goes through (1, 7) and (3, -3) _____________