Name:
____________
Date:
CC Algebra -Take Home Quest on Functions - Rules at End of Quest
54 points
Mrs. Kamerer
If the domain of the function, g ( x)  2 x 2  1 is {-1, 0, 1}, find g (1), g (0), and g (1). Show
1.)
your work below.
2.)
(1.5 pts)
According to your work on the previous question, what is the range of the function,
g ( x)  2 x 2  1 , if the domain is {-1, 0, 1}?
(0.5 pts)
y
3.)
According the your work on the previous two questions, is g ( x ) continuous or discrete? Justify

your answer. (0.5 pts)



y


y
4.)


Are the following relations functions?
Justify each of your answers. (3 pts total)

a.)

b.)



c.)

x






























x




















































d.)
e.)
{(-2, 1), (-1, 1), (0, 1), (1,1)}
f.)
x
-1
f(x) 3
0
1
2
3
3
3
5.)
The Starbucks barista is taking inventory of how many much money they brought in selling
grande iced caramel macchiatos one Monday, G(x). If x is the number of grande iced caramel
macchiatos sold that Monday, what would be the most appropriate domain for the function? (0.5 pts)
6.)
A function, g, has a domain of {1, 2, 4, 5} and a range of {0, 1, 2}. Could g be represented by
{(1 ,0), (2,2), (5,1), (4, 0)}? Justify your answer. (1 pt)
7.)
Let f be a function such that f(x) = 3x - 1 is defined on the domain, 1 ≤ x ≤ 3. What is the range of
this function? (1 pt)



Based on
8.)
the graph of the function, f ( x)  x3  3x 2  2 , on a restricted domain, as shown
below, answer
the following questions.




x

















a.)
What
is the domain? (0.5 pts)
b.)
What
is the range? (0.5 pts)
c.)

What is the minimum value? (0.5 pts)

d.)
What is the maximum value? (0.5 pts)

e.)
What is the initial value? (0.5 pts)
f.)
What is the y-intercept? (0.5 pts)
g.)
How many x-intercepts are there? (0.5 pts)
h.)
Evaluate each of the following. Illustrate with a point on the graph. (2 pts)
f ( 1)
f (0)
f (1)
f (3)
i.)
For what values of x does f ( x)  2 ?(1 pts)
j.)
What ordered pair is shown by the notation, f (0.5)  1.375 ?
k.)
3
2
Is the function, f ( x)  x  3x  2 on the restricted domain in this problem, continuous or
discrete? Justify your answer. (0.5 pts)
(0.5 pts)
9.)
Let f ( x)  x  1 and h( x)  2 x . Find the value of each below. First, get your answer by
substituting in x = 1 and then combining the answers. Second, combine the functions first, and then
substitute in x = 1. (4.5 pts in all)
a.)
f (1)  h(1) .
Method 1(0.5 pts)
b.)
h(1)  f (1)
Method 1(0.5 pts)
c.)
Method 2(1 pt)
Method 2(1 pt)
f (1)  h(1)
Method 1(0.5 pts)
Method 2(1 pt)
10.)
If g ( x)  2 x  1 , find an expression for each function below, using the given input. Simplify
your answers. (0.5, 1, 1.5 pts --- total of 3 pts)
a.)
g (a)
b.)
g (2a )
c.)
g ( a  b)
11.)
Amanda makes friendship bracelets and sells them at a craft fair to raise money for Make a Wish
Foundation. She charges everyone $1 per order, plus $2 for each bracelet they purchase. Using the
slope-intercept form for a linear equation, C(x) = mx + b, where C(x) represents what Amanda charges a
customer at the craft fair, and x represents the number of bracelets sold for each order, answer the
questions that follow. She has a total of 124 bracelets available for sale.
a.)
What are the domain and range of this word problem? (1 pt)
b.)
What does the $1 represent in our general equation, C(x) = mx + b? (0.5 pt)
c.)
What does the $2 represent in our general equation, C(x) = mx + b? (0.5 pt)
d.)
Substituting in our answers to parts b and c of this problem, what does our general equation,
C(x) = mx + b, become? (1 pt)
e.)
What is the meaning of C(5)? Evaluate C(5). (1 pt)
f.)
What is the meaning of C(n)=25? Solve for n. (1 pt)
12.)
Use the formula for the average rate of change that Mrs. Kamerer has told you to memorize to
get the average rate of change between each of the two given points below. You must simplify your
final answer to earn full credit. You must write the formula each time. Take the coaching. Writing it
over and over will help it sink in! (1 each --- 4 pts)
a.) (-1, 2), (-1, 5)
b.) (3, 4), (0, 1)
c.) (-1, 3), (2, -5)
d.) (-2, -1), (3, -1)
13.)
Graph each line on the coordinate plane provided below each problem. (0.5, 0.5, 1 --- 2 in all)
a.)
y=3
b.)
x = -2
c.)
f(x) = 
1
x3
2
Note: This will be graded in a creative way. If every question is completed, you earn 20 points. Then
there are 34 points that can be earned for correctness. Therefore, your score will be out of 54. There
will be no curve since it's a take home. It is expected that you help one another, but don't do the work
for one another. It is your responsibility to make sure you understand what another student helps you
with because I will put questions on this material on the end of the unit test, but it's too much material
not to do a checkpoint quest to make sure you are understanding the work.