Review of Functions and Transformations
Name_________________________
Terms/Concepts You Need to Know - coordinate plane, the quadrants, the x-axis, the y-axis, the
origin, x-coordinate, y-coordinate, relations, functions, vertical line test, domain, range, mapping,
graph, order of operations, how to evaluate a function, linear functions, coefficients, the parent
functions, tranformations of the parent functions
1.
2.
Label the quadrants, axes, and origin on the
coordinate plane to the right.
4
2
Plot the points on the coordinate plane.
A (0, 3) B (-2, 4) C (1, -5) D (-3, -1)
-5
5
-2
-4
-6
--------------------------------------------------------------------------------------------------------------------2
For Questions 3-7, evaluate if f ( x)  3x  1 , g ( x)  x 2  8 and h( x) 
.
x3
3. f (2)
4. g (1)
5. h(3)
6. g ( 3)
7. h(3)
--------------------------------------------------------------------------------------------------------------------For Questions 8-14, is the relation a function?
8.
9.
10.
11.
4
4
4
4
2
2
2
2
-5
5
-5
5
-5
5
-5
5
-2
-2
-2
-2
-4
-4
-4
-4
-6
-6
-6
-6
12.
{(2,3), (2, 4), (7,10)}
13.
{(3, 0), (4, 0), (5, 0), (6,1)}
x
1
2
3
4
14.
y
1
2
3
4
--------------------------------------------------------------------------------------------------------------------For Questions 15-21, name the parent function of the function whose equation is given.
15. j ( x)  x  1
16. k ( x) 
2
x 1
5
17. l ( x) 
7 2
x
3
18. m( x)  
9
8
2x
1
2
19. n( x)   x3  11
20. p( x)  400 x
21. q ( x)   x  7
4
13
--------------------------------------------------------------------------------------------------------------------22.
True or False: All functions are relations.
23.
In what quadrant is the point whose coordinates are (-3, 9)?
24.
On which axis is the point whose coordinates are (0, 1)?
For Questions 25-32, describe the transformation in relation to the parent function.
25. r ( x) 
2
x
5
29. v( x)  9 x
28. u ( x ) 
26. s ( x)   x  1
27. t ( x)  10 x 2  9
30. w( x)  x  12
1
31. b( x)   x  1.3
5
9 3
x
2
4
32. c( x)   x
3
--------------------------------------------------------------------------------------------------------------------For Questions 33-38, match the equation for the function on the left with its graph on the right.
33.
34.
d ( x)   x 2  3
A)
B)
f ( x)  4 x 2  3
4
4
4
2
2
2
-5
35.
36.
37.
5
g ( x)   x 2  3
1
h( x )   x 2  3
4
-5
5
-2
-4
-4
-4
-6
-6
-6
E)
F)
4
4
4
2
2
2
5
k ( x)  4 x 2  3
5
-2
D)
j ( x)  x 2  3
-5
-2
-5
38.
C)
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
--------------------------------------------------------------------------------------------------------------------For Questions 39-41, name the parent function, and describe the transformation in relation to the
parent function.
39.
40.
41.
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
Review of Reasoning & Logic
Name_________________________
Provide a counterexample for the following false statements.
1.
If it has four wheels, then it is legal to drive it
on the interstate.
1.______________________
2.
All movies are made by Disney.
2.______________________
3.
If it is a country in North America, then it is the United
States.
3.______________________
4.
If a car has a siren, then it is a police car.
4.______________________
--------------------------------------------------------------------------------------------------------------------5.
What is the hypothesis of the statement below?
If it is green, then it is an infection.
5.______________________
--------------------------------------------------------------------------------------------------------------------6.
What is the conclusion of the statement below?
If he is running, then go get him.
6.______________________
--------------------------------------------------------------------------------------------------------------------7.
Write the statement below in if-then form.
Boys have cooties.
7.__________________________________
_________________________________
--------------------------------------------------------------------------------------------------------------------8.
Write the converse of the statement below.
If the clock strikes 12, then you are dead.
8.__________________________________
_________________________________
--------------------------------------------------------------------------------------------------------------------9.
Write the contrapositive of the statement below.
If you play Guitar Hero, then you rock.
9.__________________________________
_________________________________
--------------------------------------------------------------------------------------------------------------------10.
Write the inverse of the statement below.
If you teach math, then you are beautiful. 10._________________________________
__________________________________
--------------------------------------------------------------------------------------------------------------------11.
What is the contrapositive of the conditional statement below?
If we do not help them, then we will regret it for the rest of our lives.
--------------------------------------------------------------------------------------------------------------------12.
Give a counterexample for the false statement below.
If it is a word in the English language with exactly three letters, then it has exactly one
vowel in it.
--------------------------------------------------------------------------------------------------------------------13.
Is the example below a use of inductive or deductive reasoning?
Over the course of three years, I have seen six movies starring Tom Hanks. I think every
one of the movies is an awesome movie. I now tell my friends, “If a movie has Tom
Hanks in it, then it is an awesome movie!”
14.
Write the conclusion of the statement below.
If there is lightning, then you hear thunder.
--------------------------------------------------------------------------------------------------------------------15.
Write the statement in If-Then form.
Jeans are blue.
--------------------------------------------------------------------------------------------------------------------16.
Write the converse of the statement below.
If you clean your room, then you can go to the movies.
--------------------------------------------------------------------------------------------------------------------17.
Give a counterexample for the false statement below.
If is a month on the calendar, then it has 31 days in it.
--------------------------------------------------------------------------------------------------------------------18.
Is the example below a use of inductive or deductive reasoning?
Jeff goes to Las Vegas, and he sits down at a Blackjack table. Jeff ends up winning each
of the first five games he plays. He then throws up his arms in glee and says, “I will
never lose at this game.”
--------------------------------------------------------------------------------------------------------------------19.
Write the inverse of the statement below.
If it’s the end of the world as we know it, then I feel fine.
--------------------------------------------------------------------------------------------------------------------20.
Is the example below from the movie Forrest Gump a use of inductive or deductive
reasoning?
Jenny tells Forrest to run if he’s ever in trouble. During the war in Vietnam, Forrest gets
in trouble, so he starts running.
--------------------------------------------------------------------------------------------------------------------21.
Give a counterexample for the false statement below.
If it is an item with strings, then its primary use is as a musical instrument.
--------------------------------------------------------------------------------------------------------------------For Questions 22-23, fill in the appropriate truth values into the table below:
Conditional Statement
True
Inverse
False
Converse
22.
Contrapositive
23.
--------------------------------------------------------------------------------------------------------------------24.
Fill in the blanks: The inverse of a conditional statement is formed by ______________
the _____________ and the ______________.
25.
Fill in the blanks: The converse of a conditional statement is formed by _____________
the ____________ and the ______________.
--------------------------------------------------------------------------------------------------------------------26.
Assume that a conditional statement is false.
A)Is the inverse false?
B)Is the converse false?
C)Is the contrapositive false?
Review on Function Characteristics
Name_________________________
For the graph of the function, find the following: domain, range, intervals of increase and
decrease, maximum, minimum, x and y-intercepts, and solutions (or zeros). In addition, state
whether the function is “even”, “odd”, or “neither”. Do not find the intervals of increase and
decrease for #5.
1.
2.
3.
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
4.
5.
6
6
4
4
2
2
-5
5
6.
-5
5
-2
-2
-4
-4
-6
-6
7.
8.
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
9.
On the front side, which of the functions graphed are discrete? Which are continuous?
Question 6 is neither discrete nor continuous.
-------------------------------------------------------------------------------------------------------------------For Questions 10-15, state if the function whose equation is given is “even”, “odd”, or “neither”.
10. f ( x)  x5
11. g ( x)  9 x
12. h( x)  x 2  10
13. j ( x)  x  6
14. k ( x)   x  1
15. l ( x )  x
--------------------------------------------------------------------------------------------------------------------For Questions 16-18, state the x and y intercepts for the function whose equation is given.
16. y 
1
x
2
17. y  4 x  3
18. y  2 x  30
19.
How does one find the solutions or zeros of a function using the equation like in
Questions 16-18?
--------------------------------------------------------------------------------------------------------------------Match the description of the function with its graph. For the one description without a graph
pictured, write "NONE."
A)
B)
__________20. The profit for the athletic department
from selling biscuits for breakfast is a function of the
amount it charges for the biscuits.
__________21. In The Curious Case of Benjamin
Button, Benjamin's body gets younger over time. So,
the age of his body is a function of time.
C)
D)
__________22. The likelihood of having lung cancer
in one's life is a function of the number of cigarettes
smoked in one's life.
__________23. The height of a basketball dropped
from one's hands on a gym floor is a function of time.
__________24. The volume of a cubical box is a
function of the length of one of its sides.
Review of Rates of Change/Sequences
Name_________________________
Using the graph of the function, A)state if it has a constant rate of change or a variable rate of
change. B)If it has a constant rate of change, compute the rate of change.
1.
2.
3.
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
4.
5.
6.
6
6
6
4
4
4
2
2
2
-5
5
-5
5
-5
5
-2
-2
-2
-4
-4
-4
-6
-6
-6
--------------------------------------------------------------------------------------------------------------------A)Compute the rate of change over the requested interval. B)Based on the list of ordered pairs,
does the function have a constant rate of change or a variable rate of change?
7. from x = 3 to x = 7
{(5,11), (3, 21), (7, 26)}
8. from x = 0 to x = 3
9. from x = -3 to x = 6
x
n( x )
x
-3
0
6
12
0
10
p( x)
-5
-11 -23 -35
1
8
2
6
3
4
--------------------------------------------------------------------------------------------------------------------For Questions 10-15, find the value of the desired term in the sequence based on its recursive or
closed end definition.
10.
closed form: tn  4n
What is the value of the 1st term?
11.
recursive: t1  1; tn  tn1  9
What is the value of the 3rd term?
12.
closed form: an  2n  6
closed form: tn 
15.
closed form: an  n 2  3
What is the value of the 8th term?
14.
recursive: t1  5; tn  4  tn1  1
1
n 1
2
What is the value of the 6th term?
13.
What is the value of the 4th term?
What is the value of a11 ?
--------------------------------------------------------------------------------------------------------------------Write the recursive definitions for the following sequences.
1
, ...
3
16.
4, 5, 6, 7, 8, 9, ...
17.
27, 9, 3, 1,
18.
2, -8, 32, -128, ...
19.
0, -8, -16, -24, -32, ...
20.
2, 3, 5, 9, 17, 33, 65, ...
21.
8, 12, 18, 27, 40.5, 60.75, ...
--------------------------------------------------------------------------------------------------------------------For Questions 22-27, write the closed form definition for the sequence.
22.
3, 4, 5, 6, ...
23.
19, 15, 11, 7, ...
24.
0, -12, -24, -36, ...
25.
-6, 1, 8, 15, ...
26.
7, 9.5, 12, 14.5, ...
27.
13, 13, 13, 13, ...
--------------------------------------------------------------------------------------------------------------------28.
In the back of the Krispy Kreme bakery, doughnuts are being prepared to be sold. A
worker requires twenty minutes to complete a batch of 240 doughnuts. In the next 30
minutes, the worker completes a new batch of 300 doughnuts.
A)What was the rate at which doughnuts were completed in the first twenty minutes?
B)What was the rate at which doughnuts were completed in the next thirty minutes?
C)During which time interval was the worker more efficient?
--------------------------------------------------------------------------------------------------------------------For Questions 29-30, write the first three terms of the infinite sequence based on the closed form
definition.
29.
an  5n  8
30.
tn  3n 2