Math 1111 Review Sections 1.1-1.3 Ralston
ANSWER KEY
You may use your formula sheet and a TI-83 or equivalent calculator. Sharing of calculators is not permitted
For questions 1-2, complete the table. Use the resulting solution points to sketch the graph of the equation.
1. y = 3x - 6
|
x |
y |
|
-1
|
-9 |
|
0
|
-6 |
|
2
|
0 |
2. 
|
x |
y |
|
-2
|
8 |
|
-1
|
5 |
|
0
|
4 |
|
1
|
5 |
|
2
|
8 |
For questions 3-5, use the following table
|
U.S. Presidents and Their Vice Presidents |
|
|
President (x) |
Vice President (y) |
|
George Washington |
John Adams |
|
John Adams |
Thomas Jefferson |
|
Thomas Jefferson |
Aaron Burr |
|
Thomas Jefferson |
George Clinton |
|
James Madison |
George Clinton |
|
James Madison |
Elbridge Gerry |
3. Determine whether the relation is a function NO, since Thomas Jefferson had 2 different VPs as well as James Madison
4. State the domain of the relation. {George Washington, John Adams, Thomas Jefferson, James Madison}
5. State the range of the relation. {John Adams, Thomas Jefferson, Aaron Burr, George Clinton, Elbridge Gerry}
For questions 6-8, use the following list of ordered pairs. Each ordered pair represents year as x and number of North Atlantic tropical storms and hurricanes as y.
{(1994, 7) (1995, 19) (1996, 13) (1997, 7) (1998, 14) (1999, 12) (2000, 15) (2001, 15) (2002, 12)}
6. Determine whether the relation is a function. YES
7. State the domain of the function. {1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002}
8. State the range of the function. {7, 12, 13, 14, 15, 19}
For questions 9-, consider the following relation and
its graph: y = 
9. Find the y-intercept of the relation. Write answer as an ordered pair . (0,0)
10. Does the given relation represent a function? How do you know? Yes, the graph PASSES VLT
11. What is the domain of the function? Write answer in interval notation. (-∞, ∞)
12. What is the range of the function? Write answer in interval notation. (-∞, ∞)
13. Observe the graph (graphically). Does the function appear to be even, odd, or neither? Odd
14. Confirm your answer to question #13, algebraically.
-y =(-x)3 -3(-x)
-y = - x3 + 3x
-1* -y =-1*(- x3 + 3x)
y = x3 - 3x same as original given equation, therefore, it is ODD.
15. Determine the x-intervals for which the function is increasing. Write answer in interval notation. (-∞, -1) or (1, ∞)
16. Determine the x-intervals for which the function is decreasing. Write answer in interval notation. (-1, 1)
17. Identify the relative minimum(s), if any exist. Write answer as ordered pair. (1, -2)
18. Identify the relative maximum(s), if any exist. Write answer as ordered pair. (-1, 2)
19. Observe the graph (graphically). Estimate the zeros (x-intercepts) of the function. Write answer as an ordered pair.
(-1.7, 0) (0, 0) (1.7, 0)
20. Confirm your answer to question #20, algebraically. Write answer as an ordered pair.
y = x3 -3x
y = x(x2 - 3)
So either x = 0 or x2 - 3 = 0
x2 = 3
x = square root of 3 and -square root of 3
(-sqrt 3, 0) (0, 0) (sqrt 3)
For questions 21-23, evaluate the given function at the given values of the independent variable and simplify.
21. f(2) = 11/4
22. f(0) = not possible, can NOT have zero in the denominator
23. f( -x) = 2x2 +3 / x2