Project AMP
Dr. Antonio Quesada – Director, Project AMP
Domain and Range
1. The domain of a function described by this set of ordered pairs in (x, y)-form:
{(-2, 4), (-1, 1 ), (0, 0), (1, 1). (2, 4)} is {-2, -1, 0, 1, 2} What variable does the
domain represent?
2. Find the domain of the function described by this set of ordered pairs:
{(-3, 6), (-1, 2), (5, -10), (0, 0), (2, -4), (3, -6), (4, -8)}
3. The range for the ordered pairs in #1 is {4, 1, 0, 1, 4}. What variable does the
range represent?
4. Find the range of the function described by the set of ordered pairs in #2.
5. The domain is the set of values assigned to x, the range is the set of
corresponding values of y. Find the domain and range for the following set of
ordered pairs:
{(2, 4), (5, 9), (a, b), (-6, 4), (7, -12), (-p, q), (0, 0)}
Domain:
Range:
6. Look at the following graph:
Is there a point that corresponds to x = -1? Is -1 in the domain of the graph of this
function?
Is there a point that corresponds to x = 5? Is 5 in the domain of the graph of this
function?
Project AMP
Dr. Antonio Quesada – Director, Project AMP
For a graph of a function, the domain is any value of x for which there is a
corresponding value of y, hence, a point on the graph.
The domain for the function represented by this graph is all real numbers > 1.
7. Refer to the graph in #6. Is there any point that corresponds to y = -2? Is -2 in the
range of the graph of this function?
Is there a point that corresponds to y = 10? Is 10 in the range of the graph of this
function?
What is the range of the function represented by the graph?
8. Find the domain and range of the functions described by the following graphs.
A
B
Domain A =
Domain B =
Range A =
Range B =
C
Domain C =
D
Domain D =
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Range C =
Range D =
E
F
Domain E =
Domain F =
Range E =
Range F =
G
H
Domain G =
Domain H =
Range G =
Range H =
When a function is given as a rule, y is a function of x and is written as y = f(x).
The variable x is called the independent variable because you can choose the
value of x you want to evaluate. The domain is the set of permissible values of x.
The range is the set of all the possible values you can get out of the function. We
call y the dependent variable because it depends on the value of x that you
choose.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
9. Graph the functions, then state the domain and range for each.
a) y = xsinx
Range =
Domain =
b) y = 4sinx
Range =
Domain =
10. For many functions, the domain is the set of all real numbers but sometimes there
are values for x that won’t work. Determine which values of x are not in the
domain of the following functions.
a) y = 1/x
b) y = 5/(x +3)
c) y = (3+x)/x2
d) y =
e) y =
x2 − 9
x −3
− x +3
f) y = 2 x
g) y =
5 x − 12
h) y =
3− x
11. What arithmetic principle did you use to answer a, b, c, and d ?
12. What arithmetic principle did you use to answer e, f, g, and h?
The domain of a function is the set of all real numbers except for the values of x
that do not give real solutions.
13. Graph the function in #10 on your calculator. What is the range for each of the
functions?
a)
g)
b)
h)
c)
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d)
e)
f)
Dr. Antonio Quesada – Director, Project AMP