Section 2.4: Functions
Learning Objectives:
1. Identify the graph of a function
2. Determine the domain and range of a function
3. Use function notation and evaluate functions
4. Read and interpret information given graphically
Distinguish the Graph of a Function from that of a Relation
Functions (example) TL
Example: Three different relations are given in mapping notation below. Determine
whether each relation is a function.
Example: Determine whether the relation given is a function.
f ={ (19, 500), (20, 630), (21, 525), (21, 540), (22, 550)}
Vertical Line Test
Example: Use the vertical line test to determine if any of the relations shown are
functions.
a.
b.
Example: Use a table of values to graph the relation defined by y  2 x  3 , then use
the vertical line test to determine whether the relation is a function
x
y = |2x|-3
Domain and Range of a Function
Example: Use a table of values to graph the functions given. Then use boundary lines
to determine the domain and range of each.
b. y  x 3
a. y  x
y x
x
x
y  x3
Example: Use a table of values to graph the relations given. Then use boundary lines
to determine the domain and range.
a. y 
x 1
x  5x  6
2
b. y  8  x
c. y  9  x2
Use Function Notation and Evaluate Functions
Definition: “y is a function of x” can be represented as y  f ( x) using
function notation. The letter f is used to represent a sequence of
operations to be performed on x.
Example: Given g ( x)  x2  2 x  8 determine the value of each, then simplify.
a. g  4 
b. g  6 
c. g  k 
d. g  3a 
e. g  a  h 
Reading and Interpreting Information Given Graphically
The following statements are synonymous:
1.
2.
3.
f  2   5
 2, f  2    2,5
 2,5
is on the graph of f
4. when x  2 , f  x   5
Example: For the function f whose graph is shown
a. State the domain of the function.
b. Evaluate the function at x = 2.
c. Determine the value(s) of x for which y = 2.5.
d. State the range of the function.
e. What is the value of f  3 ?
f. What values of x satisfy f  x   0?
Example: When Maurice calls his friend Gaston in France, he pays 20¢ for every
minute he talks plus a flat surcharge of $5.00 per call.
a. Write this relation in function form.
b. Find the cost if a single call lasted 30-min.
c. Determine how long a call lasted if it cost $18.60 to make.
d. Determine the domain and range of the function in this context, if Maurice’s budget
limits him to spending at most $30 per call