Name ______________
Period ___ Teacher:__________ Date ______
Algebra 2 Unit 3 Model Curriculum Assessment
1.
Indicate whether each statement is true for all functions of x in the
xy-plane by checking the appropriate box in the table below.
True of
All Functions
No vertical line drawn through the
graph of a function will intersect it
more than once.
No horizontal line drawn through the
graph of a function will intersect it
more than once.
Each y-value of a function is
mapped to exactly one x-value.
Each x-value of a function is
mapped to exactly one y-value.
Not True of
All Functions
2.
Use the tables below to create two quantitative relationships. Use the
first table to create a quantitative relationship that is a function of x,
and use the second table to create a quantitative relationship that is
NOT a function of x. Beside each table, explain why the corresponding
quantitative relationship is or is NOT a function of x.
Function of x
x
y
NOT a Function of x
x
y
3.
Indicate whether each quantitative relationship is a function of x
by checking the appropriate box in the table below.
Is a
Function of x
Is Not a
Function of x
4.
The Chang family is on their way home from a cross-country road trip.
During the trip, the function D t   2,280  60t can be used to model
their distance, in miles, from home after t hours of driving.
Part A Find D 15 and interpret the meaning in the context of the
problem.
Part B If D t   1,200, find the value of t and interpret its meaning in
the context of the problem.
5.
The function F v  represents the amount, in dollars, raised at a
fundraiser for a charity by v volunteers. Use function notation to write
a representation of each of the following.
Part A The amount, in dollars, raised by 12 volunteers.
Part B The amount, in dollars, raised by m volunteers is $2,500.
Part C The amount, in dollars, raised by v volunteers is at least
$3,000.
Part D 90 percent of the amount, in dollars, raised by 30 volunteers.
6.
In New Jersey, the 2009 tuition cost at public universities for each
student who lives in state was $17,547. In-state students paid 70% of
the tuition amount, and the rest was paid by the state.
Part A Use function notation to express the total amount of tuition
paid by the state for all in-state students as a function of the
number of in-state students. Explain how any variables used
are defined in the context of the problem. Show your work.
Part B In 2009, there were 69,543 in-state students enrolled at public
universities in New Jersey. Use your function from Part A to
find the total amount of tuition paid, in dollars, by the state for
the 69,543 in-state students. Show your work.
7.
In the following, assume x is the independent variable and y is the
dependent variable.
Part A Use the definition of function to explain why the relation shown
in the table below is a function.
x
0
2
3
4
5
6
y
0
3
2
10
10
2
Part B Write the domain of the function.
Part C Write the range of the function.
8. The graph below describes the labor cost for a mechanic.
Which of the following describes the domain of the function?
a.
b.
c.
d.
All
All
All
All
real numbers
real numbers greater than or equal to 0
whole numbers greater than 1
whole numbers greater than 75
9. The function f t   7.2t models the average distance, f t  , in kilometers
that Bob rides his bike over time, t, in hours.
The function g t   5.9t models the average distance, g t  , in
kilometers that Alice walks over time, t, in hours.
Part A What are the domains of the two functions?
Part B Graph the two functions on the coordinate plane below.
Part C Compare the rate of change of f t  to the rate of change
of g t  . What does this tell you about Alice’s and Bob’s speeds?
Part D Is there a time where Bob’s and Alice’s distances are the same?
Explain.
10.
2, 6, 18, 54, 162,
The first five terms of a geometric sequence are given above. Write a
recursive function rule for the sequence.
 1
an  9   
 3
11.
n
Fill in the blanks to give a recursive function for the sequence defined
explicitly above.
f 1  _____________
f  n  _____________, _______
12.
The first term in a sequence is 18, and each term after the first is 4
times the preceding term.
Part A Which of the following recursive functions defines the sequence
described above?
a.
b.
c.
d.
f 1  18
f  n   4f  n  1 , n  1
f 1  18
f  n   4  f  n  1 , n  1
f 1  18
f  n   4f  n  1 , n  1
f 1  18
f  n   4  f  n  1 , n  1
Part B Which of the following explicit functions defines the sequence
described above, where n is a positive integer?
a.
f  n   18  4
b.
f  n   18  4
c.
f  n  18  4
d.
f  n  18  4
n
n 1
n
n 1
13.
A ball is dropped, and for each bounce after the first bounce the ball
reaches a height that is a constant percent of the preceding height.
After the first bounce it reaches a height of 10 feet, and after the third
bounce it reaches a height of 4.9 feet.
Part A: The height the ball reaches after the nth bounce is represented
by an below. Write the value for each an below.
a1  10 feet
a2  _____
a3  4.9 feet
a4  _____
a5  _____
Part B: Write an explicit rule for the height after the nth bounce, an ,
where n represents the bounce number.
Explicit rule: ____________________
14.
A job pays a salary of $8.50 an hour for the first year and $8.85 an
hour for the second year. The hourly salary for year n follows an
arithmetic sequence.
Part A: Write a recursive rule for the hourly salary.
Part B: Write an explicit rule for the hourly salary.
15.
For the pattern above, the total number of boxes used in Figure n can
be described by a geometric sequence. Write a recursive formula to
find the number of boxes in Figure n.
Recursive formula: ____________________
16.
a1  200
an 1 
an
, n 1
4
A recursive formula for a sequence is given above. Write an explicit
formula for the sequence.
Explicit formula: ____________________
17.
Write an expression for the inverse of f  x  
5x
 9.
6
f 1  x   ____________________
18.
Which of the following is the inverse function for f  x  
where x  0 ?
a.
f 1  x    4x  1
b.
f 1  x   4x  1
c.
f 1  x   4x  1
d.
f 1  x   2 x  1
2
x2  1
,
4
19.
If f  x  
3
, find f 1  x  , where x  2. Show your work.
x 2
f 1  x   ____________________
20.
Which of the following is the inverse function for f  x  
x2  1
,
4
where x  0 ?
21.
a.
f 1  x    4x  1
b.
f 1  x   4x  1
c.
f 1  x   4x  1
d.
f 1  x   2 x  1
2
If f  x  
3
, find f 1  x  , where x  2. Show your work.
x 2
f 1  x   ___________________