Name: ______________________________
Math 412- Ms. Castellano
Date: ____________
Practice
Show all work to receive full credit.
1. Which of the following relations is not a function?
1.
2.
3.
4.
{(1, 6), (5, 6), (1, -3), (-2, 4)}
{(1, 6), (2, 6), (-3, 6), (7, 6)}
{(9, 0), (8, -4), (-4, 6), (1, 0)}
{(-11, 2), (2, -11)}
2. Which of the following relations is a function?
1.
2.
3.
4.
{(0, 6), (5, 6), (1, -3), (0, 4)}
{(1, 6), (2, 6), (4, 8), (-7, -2)}
{(9, 0), (8, -4), (8, 6), (-3, 0)}
{(-11, 2), (2, -11), (9,-12), (2, -1)}
3. The relation {(-1, 1), (8, -2), (5, 6)} is a function. Which of the ordered pairs below could be
added to this relation and it would no longer be a function?
1.
2.
3.
4.
(1, 6)
(-5, 2)
(2, 1)
(8, -8)
4. Which graph represents a function?
1.
3.
2.
4.
5. Bill is remodeling his house and intends to put a ceiling fan in each room of the house. Ceiling
fans are on sale this week for $49, including tax. He has $300. If the function f(c) = 49c models
the situation, what is the domain of the function in the context of the problem?
1.
2.
3.
4.
0≤c≤6
0≤c≤7
{0, 1, 2, 3, 4, 5, 6}
{0, 49, 98, 147, 196, 245, 294}
6. The temperature in the pool at Yasmin’s house is 68°. She is having a swim party tomorrow, so
her dad turned on the pool heater, which heats the water 2° each hour. Which function describes
the temperature of the pool water over time?
1.
2.
3.
4.
f(x) = 16x + 68
f(x) = 2x + 68
f(x) = 2 + 68
f(x) = 68
7. If
, find the value of f(3).
1. 4
2. 16
3.
4.
8. Given: the function f defined by f(x) = 3x2 − 4. Which statement is true?
1.
2.
3.
4.
f(0) = 0
f(-2) = f(2)
f(5) + f(2) = f(7)
f(5) · f(2) = f(10)
9. The accompanying graph shows the heart rate, in beats per minute, of a jogger during a 4minute interval. What is the range of the jogger’s
heart rate during this interval?
1.
2.
3.
4.
0–4
1–4
0–110
60–110
10. A bug travels up a tree, from the ground, over a 30-second interval. It travels fast at first and
then slows down. It stops for 10 seconds, then proceeds slowly, speeding up as it goes. Which
sketch best illustrates the bug’s distance (d) from the ground over the 30-second interval (t)?
1.
3.
2.
4.
11. What are the domain and the range of the function shown
in the graph below?
1.
2.
3.
4.
{x | x > −4}; {y | y > 2}
{x | x ≥ −4}; {y | y ≥ 2}
{x | x > 2}; {y | y > −4}
{x | x ≥ 2}; {y | y ≥ −4}
12. If h(x) = x + 5 and g(x) = -2x2, find h(5) + g(2).
) 2 3 x − 4 − 24 .
13. Given f ( x=
a. Evaluate f(0)
b. Solve f(x) = 0
14. Graph each function.
f(x) = 3𝑥 − 2; D:{-4, -2, 0, 2}
f(x) = 3𝑥 − 2; D: -2 ≤ 𝑥 ≤ 2
f(x) = 3𝑥 − 2; D: ℝ
15. A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on
the ground. The graph below shows the height, y, of the ball from the ground after x seconds.
a. What is the independent variable?
b. What is the dependent variable?
c. What is the domain of the function?
d. For which interval is the ball’s height always decreasing?
(1)
(2)
0 ≤ x ≤ 2.5
2.5 < x < 5.5
(3)
(4)
0 < x < 5.5
x≥2
e. For which interval is the ball’s height always increasing?
(1)
(2)
0 < x < 2.5
2.5 < x < 5.5
(3)
(4)
0 < x < 2.5
x≥2
16. Use the given graph of f(x) to find the following:
a. the domain
b. the range
c. f(0) + f(2)
d. f (−4) − f (4) ⋅ f (5)
e. the average rate of change between x = 0 and x = 5.
17. If the function h(x) represents the number of full hours that it takes a person to assemble x
tires in a factory, which would be an appropriate domain for the function?
(1)
(2)
(3)
(4)
the set of real numbers
the set of negative integers
the set of integers
the set of non-negative integers
18. The statement f(-1) = 5 implies which of the following to be true?
(1)
(2)
(3)
(4)
5 is in the domain and -1 is in the range
The point (-1, 5) would appear on the graph of this function
The point (5, -1) would appear on the graph of this function
Both -1 and 5 are elements in the range of this function
19. In the table below, what is the average rate of change in
temperature over the interval from 5 to 15 minutes?
(1)
(2)
-1.5oC/minute
-2oC/minute
(3)
(4)
-3oC/minute
-2.5oC/minute
Time (minutes)
0
5
10
15
20
Temperature (oC)
75
60
50
45
35
20. The Lombardo family is taking a trip. The graph below shows how their distance from home
changed over time.
a. Calculate the rate of change during each time interval.
b. During which time interval(s) did the greatest rate of change occur?
c. During which time interval(s) were the rates of change the same?