Algebra II
Name _______________________Per_____
Test Review Module 1
Composite Functions
Find the following function values
g x 
f  x   2x  1
x3
2
h  x   x
j  x   2x  5
1.
 g f1
2. h  g  0  
3.
f(5)
h( 3)
4. g(-11) + j(2)

6. j f  x 
5. g  j  x  

Complete each domain with the given notation:
7. Inequality:
𝒙 ≥ −𝟑
8. Inequality:________________
Set Notation:________________
Set Notation: ________________
Interval Notation:_____________
Interval Notation:
9. Inequality:
Set Notation: {𝒙|𝒙
(-∞, 6]
10. Inequality:________________
> 𝟒}
Interval Notation:_____________
Set Notation: ________________
Interval Notation:
[-3, 6)
Find the following:
11.
12.
As x   , f ( x )  _________
As
As x   , f ( x )  _________
As
x   ,
x   ,
f ( x )  _________
f ( x )  _________
Domain ___________________
Domain ___________________
Range ____________________
Range ____________________
Min value ___________________
Max value __________________
The graph is increasing over the interval
The graph is increasing over the interval
______________________________
______________________________
The graph is decreasing over the interval
The graph is decreasing over the interval
______________________________
______________________________
The function is positive over the interval
The function is positive over the interval
______________________________
______________________________
The zero(s) of the function are
The zero(s) of the function are
______________________________
______________________________
What is the average rate of change
over the interval x = 0 to x = 2
What is the average rate of change
over the interval x = 2 to x = 7
______________________________
______________________________
13.
14.
As , x   f ( x )  _________
Domain ___________________
As x   , f ( x )  _________
Range ____________________
Domain ___________________
Min value ___________________
Range ____________________
Max value ___________________
Min value __________________
The graph is increasing over the interval
The graph is increasing over the interval
______________________________
______________________________
The graph is decreasing over the interval
The graph is decreasing over the interval
______________________________
______________________________
The function is positive over the interval
The function is positive over the interval
______________________________
______________________________
The zero(s) of the function are
The zero(s) of the function are
______________________________
______________________________
What is the average rate of change
over the interval x = 0 and x = 3
15. A motorcycle is moving in a straight line on a road. The distance traveled by
the bike at various times is shown in the table below. Find the average speed of the bike
over the interval 5 to 15 seconds.
Graphing a linear function on a restricted domain
Draw the graph of the function with its given domain. Then determine the range using interval notation.
16. g( x )  3x  2 with domain ( 1, 2] :
17. h( x )  0.5x  1 with domain ( , 4) :
Range: _________________
Range: _________________
18. Given the table for h(x) below, make a table for your new function:
y = h(x)
y = -2h(x-1) + 2
X
-2
-1
0
1
2
x
Y
2
0
-2
4
0
y
y = h(1/2x) + 3
x
Match how the following graphs are obtained from the graph of y = f(x)
_____19. y = f(x + 5)
A. horizontal stretch
B. horizontal compression
_____20. y = 5f(x)
C. translate 5 units up
D. translate 5 units down
_____21. y = f(-x)
E. reflection over the y axis
F. reflection over the x-axis
_____22. y = f(x) + 5
G. vertical compression
H. vertical stretch
_____23. y = f(5x)
_____24. y =
1
f(x)
5
I. translate 5 units to the right
J. translate 5 units to the left
y
25. Use the graph of f(x) below to complete the transformation y = f(2x) :
y = f(x)
y = f(2x)
26. Use the graph of g(x) below to complete the transformation y = 2g(x) :
g(x)
y = 2g(x)
Find the inverse of each of the following functions. Then graph the function and the inverse. Make sure you label
the function and the inverse. Then use composite functions to show they are inverses of each other.
27. f(x)  x  6
f1 (x) =________________
Proof they are inverses:
f (f 1 (x ))
and
f 1 (f (x ))
1
x 3
2
f1 (x) =________________
29. f(x) = 2x +10
f1 (x) =________________
28. f(x) 
Proof they are inverses:
f (f 1 (x ))
f 1 (f (x ))
Proof they are inverses:
f (f 1 (x ))
30. Use composite functions to prove f(x) = -2x +3 and g(x) =
and
and
f 1 (f (x ))
-x +3
are inverse functions.
2
31. If functions f(x) and g(x) are inverses of each other then f(g(x)) and g(f(x)) = ________
32. How does the graph of f(x) + 2 differ from f(x)?
A.
B.
C.
D.
The graph
The graph
The graph
The graph
of f(x) +
of f(x) +
of f(x) +
of f(x) +
2 is two units right of the graph of f(x).
2 is two units left of the graph of f(x).
2 is two units above the graph of f(x).
2 is two units below the graph of f(x).
33. How does the graph of y = f(x)– 9 differ from the graph of y = f(x) + 1?
A
B
C
D
The graph
The graph
The graph
The graph
of y = f(x) - 9 is 10 units to the right of the graph of y = f(x) + 1.
of y = f(x)– 9 is 10 units below the graph of y = f(x)+ 1.
of y = f(x)– 9 is 10 units to the left of the graph of y = f(x) + 1.
of y = f(x)– 9 is 10 units above the graph of y = f(x) + 1.
34. The minimum point on the graph of the equation
graph of the equation
A. (6, 6)
y  f (x )
is (6,-1). What is the minimum point on the
y  f (x )  5 .
B. (11, 5)
C. (6, 4)
D. (-1, -1)
35. Which statement is true about the data shown in the scatter plot
A. There is no correlation between the two sets of data
B. There is a postivie correlation between the sets of data
C. There is a negative correlation between the sets of data
D.
The correlation between the data is both postitiv and negative
36.
a. Is the relation between length and height a positive or negative correlation?
b. Write the equation for the line of best fit (Round to hundredths place).
c. Using the graph or the line best-fit predict a woman’s height from a humerus that is 32cm
long. (round to the nearest cm)
d. What would be the length of a woman’s humerus if she is 190cm tall?(round to the nearest cm)
e.
What is the “r” value (round to the hundredths place)
f. What is the significance of finding the “r” value in a linear regression problem?