Name______________________________________________
Date _____________________________ Period _______________
Other Characteristics of Functions
A Practice Understanding Task
1)
How Many People are at the Pool?
The graph below shows the number of people at a swimming pool as a function of the
number of hours since the pool opened for the day. The park is open for 10 hours.
a) Does this graph represent a function? Why or why not?
b) Write a statement using function notation for the point  2, 200  .
What is the meaning of this point?
c) There are two intervals of h when the function is increasing. Using
inequalities, write those intervals.
d) There are two intervals of h when the function is decreasing. Using
inequalities, write those intervals.
e) What is the domain of this
function?
f) What is the range of this
function?
g) P  3  _____ What does this
mean in this situation?
h) What four values for h will
make the statement P  h   200
true?
Name
Profit and Loss
The amount of profit (or loss) that your pool store makes is a function of how much the high temperature is above (or below) the
normal high temperature for that day. On the horizontal axis positive values of n represent the number of degrees that a high
temperature is above the normal high temperature for a given day, while negative values of n represent the number of degrees that a
high temperature is below normal. On the vertical axis, positive values of P(n) represent a profit for the day in dollars, negative
values of P  n  represent a loss for the day, in dollars.
2)
a) Write an inequality for the values of n for which the function P  n 
is increasing.
b) Write an inequality for the values of n for which the function P  n 
is decreasing.
c) On the graph, label the point that represents
P  10  400 . Write the meaning of this
statement.
d) Write the point whose coordinates are
 2,300 in function notation. What is the
meaning of this point?
e) Write the point whose coordinates are
 2,100 in function notation. What is the
meaning of this point?
Page 2
Name
Profit and Loss (Continued)
Intercepts
The amount of profit (or loss) that your pool store makes is a function of how much
the high temperature is above (or below) the normal high temperature for that day.
On the horizontal axis positive values of n represent the number of degrees that a
high temperature is above the normal high temperature for a given day, while
negative values of n represent the number of degrees that a high temperature is
below normal. On the vertical axis, positive values of P(n) represent a profit for
the day in dollars, negative values of P(n) represent a loss for the day, in dollars.
2) Continued

This graph crosses the horizontal axis (n-axis) at two
places. These are called the n-intercepts of the graph.

This graph crosses the vertical axis ( P  n  axis) at one
place. This is called the P  n  -intercept of the graph.
f) What value of n makes the statement P  n   800 true? What is the
meaning of your answer? Label that point on the graph.
g) Describe under what conditions your pool store will make a profit.
Write an inequality that describes your answer.
h) After n  10 the profit starts to decrease.
Why do you think this happens?
i) What are the n-intercepts of the graph?
What do these intercepts represent?
j) What is the P  n  -intercept of the graph?
What does this intercept represent?
Page 3
Name
The Never-Ending Story
Look at the graph below. What do you notice that is different from the previous graphs that
we have seen so far?
a) What do you think the arrow on the right end of the graph means?
3)
b) Is the function continuous or discrete?
c) Write a function statement for the point  2, 3 on the graph.
d) What is the domain of this
function?
e) What is the range of this
function?
f) What are the x-intercepts of the
graph? What is the value of f  x  at
the x-intercepts?
g) What is the f  x  intercept of the
graph? What is the value of x at the
f  x  intercept?
Page 4
Name
Use the following graph to answer the questions below.
a) What do you think the arrows on both ends of the graph mean?
4)
b) What is the domain of this
function?
c) What is the range of this
function?
d) What are the x-intercepts of the
graph? What is the value of g  x  at the
x-intercepts?
e) What is the g  x  intercept of
the graph? What is the value of x
at the g  x  intercept?
Use the following graph to answer the questions below.
Page 5
Name
5)
a) What do you think f  6  might equal? Explain why you think that.
b) Do you think f  10  has a value? Why or why not?
c) On what interval is the function increasing
(remember, graphs are always read left to
right)?
d) On what interval is the graph decreasing?
e) On the graph, locate the points that
correspond to the statements f  3  2 and
f  4  3 .
Page 6